Search NASA⌕ Search

SEARCH · Search NASA

Results for “Context algorithm”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Experiments with conjugate gradient algorithms for homotopy curve tracking

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Irani, Kashmira M.↗

Computational requirements for on-orbit identification of space systems

For the future space systems, on-orbit identification (ID) capability will be required to complement on-orbit control, due to the fact that the dynamics of large space structures, spacecrafts, and antennas will not be known sufficiently from ground modeling and testing. The computational requirements for ID of flexible structures such as the space station (SS) or the large deployable reflectors (LDR) are however, extensive due to the large number of modes, sensors, and actuators. For these systems the ID algorithm operations need not be computed in real-time, only in near real-time, or an appropriate mission time. Consequently the space systems will need advanced processors and efficient parallel processing algorithm design and architectures to implement the identification algorithms in near real-time. The MAX computer currently being developed may handle such computational requirements. The purpose is to specify the on-board computational requirements for dynamic and static identification for large space structures. The computational requirements for six ID algorithms are presented in the context of three examples: the JPL/AFAL ground antenna facility, the space station (SS), and the large deployable reflector (LDR).

Hadaegh, Fred Y.↗

Optimal pattern distributions in Rete-based production systems

Since its introduction into the AI community in the early 1980's, the Rete algorithm has been widely used. This algorithm has formed the basis for many AI tools, including NASA's CLIPS. One drawback of Rete-based implementation, however, is that the network structures used internally by the Rete algorithm make it sensitive to the arrangement of individual patterns within rules. Thus while rules may be more or less arbitrarily placed within source files, the distribution of individual patterns within these rules can significantly affect the overall system performance. Some heuristics have been proposed to optimize pattern placement, however, these suggestions can be conflicting. This paper describes a systematic effort to measure the effect of pattern distribution on production system performance. An overview of the Rete algorithm is presented to provide context. A description of the methods used to explore the pattern ordering problem area are presented, using internal production system metrics such as the number of partial matches, and coarse-grained operating system data such as memory usage and time. The results of this study should be of interest to those developing and optimizing software for Rete-based production systems.

Scott, Stephen L.↗

Interannual and Decadal Variability of Ocean Surface Latent Heat Flux as Seen from Passive Microwave Satellite Algorithms

Ocean surface turbulent fluxes are critical links in the climate system since they mediate energy exchange between the two fluid systems (ocean and atmosphere) whose combined heat transport determines the basic character of Earth's climate. Deriving physically-based latent and sensible heat fluxes from satellite is dependent on inferences of near surface moisture and temperature from coarser layer retrievals or satellite radiances. Uncertainties in these "retrievals" propagate through bulk aerodynamic algorithms, interacting as well with error properties of surface wind speed, also provided by satellite. By systematically evaluating an array of passive microwave satellite algorithms, the SEAFLUX project is providing improved understanding of these errors and finding pathways for reducing or eliminating them. In this study we focus on evaluating the interannual variability of several passive microwave-based estimates of latent heat flux starting from monthly mean gridded data. The algorithms considered range from those based essentially on SSM/I (e.g. HOAPS) to newer approaches that consider additional moisture information from SSM/T-2 or AMSU-B and lower tropospheric temperature data from AMSU-A. On interannual scales, variability arising from ENSO events and time-lagged responses of ocean turbulent and radiative fluxes in other ocean basins (as well as the extratropical Pacific) is widely recognized, but still not well quantified. Locally, these flux anomalies are of order 10-20 W/sq m and present a relevant "target" with which to verify algorithm performance in a climate context. On decadal time scales there is some evidence from reanalyses and remotely-sensed fluxes alike that tropical ocean-averaged latent heat fluxes have increased 5-10 W/sq m since the early 1990s. However, significant uncertainty surrounds this estimate. Our work addresses the origin of these uncertainties and provides statistics on time series of tropical ocean averages, regional space / time correlation analysis, and separation of contributions by variations in wind and near surface humidity deficit. Comparison to variations in reanalysis data sets is also provided for reference.

Robertson, Franklin R.↗

Online Photometric Calibration of Automatic Gain Thermal Infrared Cameras

Thermal infrared cameras are increasingly being used in various applications such as robot vision, industrial inspection and medical imaging, thanks to their improved resolution and portability. However, the performance of traditional computer vision techniques developed for electro-optical imagery does not directly translate to the thermal domain due to two major reasons: these algorithms require photometric assumptions to hold, and methods for photometric calibration of RGB cameras cannot be applied to thermal-infrared cameras due to difference in data acquisition and sensor phenomenology. In this paper, we take a step in this direction, and introduce a novel algorithm for online photometric calibration of thermalinfrared cameras. Our proposed method does not require any specific driver/hardware support and hence can be applied to any commercial off-the-shelf thermal IR camera. We present this in the context of visual odometry and SLAM algorithms, and demonstrate the efficacy of our proposed system through extensive experiments for both standard benchmark datasets, and real-world field tests with a thermal-infrared camera in natural outdoor environments.

Daftry, Shreyansh↗

Comment on 'Modeling of Convective-Stratiform Precipitation Processes: Sensitivity to Partitioning Methods' by Matthias Steiner

Despite the obvious notion that the presence of hail or graupel is a good indication of convection, the model results show this does not provide an objective benchmark partly due to the unrealistic presence of small amounts of hail or graupel throughout the anvil in the model but mainly because of the significant amounts of hail or graupel, especially in the tropical TOGA COARE simulation, in the transition zone. Without use of a "transition" category, it is open to debate as how this region should best be defined, as stratiform or as convective. So, the presence of significant hail or graupel contents in this zone significantly degrades its use an objective benchmark for convection. The separation algorithm comparison was done in the context of a cloud-resolving model. These models are widely used and serve a variety of purposes especially with regard to retrieving information that cannot be directly measured by providing synthetic data sets that are consistent and complete. Separation algorithms are regularly applied in these models. However, as with any modeling system, these types 'of models are constantly being improved to overcome any known deficiencies and make them more accurate representations of observed systems. The presence of hail and graupel in the anvil and the bias towards heavy rainfall rates are two such examples of areas that need improvement. Since, both of these can effect the perceived performance of the separation algorithms, the Lang et al. (2003) study did not want to overstate the relative performance of any specific algorithms.

Lang, Steve↗

Use of GOES, SSM/I, TRMM Satellite Measurements Estimating Water Budget Variations in Gulf of Mexico - Caribbean Sea Basins

This study presents results from a multi-satellite/multi-sensor retrieval system designed to obtain the atmospheric water budget over the open ocean. A combination of 3ourly-sampled monthly datasets derived from the GOES-8 5-channel Imager, the TRMM TMI radiometer, and the DMSP 7-channel passive microwave radiometers (SSM/I) have been acquired for the combined Gulf of Mexico-Caribbean Sea basin. Whereas the methodology has been tested over this basin, the retrieval system is designed for portability to any open-ocean region. Algorithm modules using the different datasets to retrieve individual geophysical parameters needed in the water budget equation are designed in a manner that takes advantage of the high temporal resolution of the GOES-8 measurements, as well as the physical relationships inherent to the TRMM and SSM/I passive microwave measurements in conjunction with water vapor, cloud liquid water, and rainfall. The methodology consists of retrieving the precipitation, surface evaporation, and vapor-cloud water storage terms in the atmospheric water balance equation from satellite techniques, with the water vapor advection term being obtained as the residue needed for balance. Thus, the intent is to develop a purely satellite-based method for obtaining the full set of terms in the atmospheric water budget equation without requiring in situ sounding information on the wind profile. The algorithm is validated by cross-checking all the algorithm components through multiple- algorithm retrieval intercomparisons. A further check on the validation is obtained by directly comparing water vapor transports into the targeted basin diagnosed from the satellite algorithms to those obtained observationally from a network of land-based upper air stations that nearly uniformly surround the basin, although it is fair to say that these checks are more effective m identifying problems in estimating vapor transports from a leaky operational radiosonde network than in verifying the transport estimates determined from the satellite algorithm system Total columnar atmospheric water budget results are presented for an extended annual cycle consisting of the months of October-97, January-98, April-98, July-98,October-98, and January 1999. These results are used to emphasize the changing relationship in E-P, as well as in the varying roles of storage and advection in balancing E-P both on daily and monthly time scales and on localized and basin space scales. Results from the algorithm-to-algorithm intercomparisons are also presented in the context of sensitivity testing to help understand the intrinsic uncertainties in evaluating the water budget terms by an all-satellite algorithm approach.

Smith, Eric A.↗

Monthly-Diurnal Water Budget Variability Over Gulf of Mexico-Caribbean Sea Basin from Satellite Observations

This study presents results from a multi-satellite/multi-sensor retrieval system design d to obtain the atmospheric water budget over the open ocean. A combination of hourly-sampled monthly datasets derived from the GOES-8 5-channel Imager, the TRMM TMI radiometer, and the DMSP 7-channel passive microwave radiometers (SSM/I) have been acquired for the combined Gulf of Mexico-Caribbean Sea basin. Whereas the methodology has been tested over this basin, the retrieval system is designed for portability to any open-ocean region. Algorithm modules using the different datasets to retrieve individual geophysical parameters needed in the water budget equation are designed in a manner that takes advantage of the high temporal resolution of the GOES-8 measurements, as well as the physical relationships inherent to the TRMM and SSM/I passive microwave measurements in conjunction with water vapor, cloud liquid water, and rainfall. The methodology consists of retrieving the precipitation, surface evaporation, and vapor-cloud water storage terms in the atmospheric water balance equation from satellite techniques, with the water vapor advection term being obtained as the residue needed for balance. Thus, the intent is to develop a purely satellite-based method for obtaining the full set of terms in the atmospheric water budget equation without requiring in situ sounding information on the wind profile. The algorithm is validated by cross-checking all the algorithm components through multiple-algorithm retrieval intercomparisons. A further check on the validation is obtained by directly comparing water vapor transports into the targeted basin diagnosed from the satellite algorithms to those obtained observationally from a network of land-based upper air stations that nearly uniformly surround the basin, although it is fair to say that these checks are more effective in identifying problems in estimating vapor transports from a "leaky" operational radiosonde network than in verifying the transport estimates determined from the satellite algorithm system. Total columnar atmospheric water budget results are presented for an extended annual cycle consisting of the months of October-97, January-98, April-98, July-98,October-98, and January- 1999. These results are used to emphasize the changing relationship in E-P, as well as in the varying roles of storage and advection in balancing E-P both on daily and monthly time scales and on localized and basin space scales. Results from the algorithm-to-algorithm intercomparisons are also presented in the context of sensitivity testing to help understand the intrinsic uncertainties in evaluating the water budget terms by an all-satellite algorithm approach.

Smith, E. A.↗

Comparison of Five System Identification Algorithms for Rotorcraft Higher Harmonic Control

This report presents an analysis and performance comparison of five system identification algorithms. The methods are presented in the context of identifying a frequency-domain transfer matrix for the higher harmonic control (HHC) of helicopter vibration. The five system identification algorithms include three previously proposed methods: (1) the weighted-least- squares-error approach (in moving-block format), (2) the Kalman filter method, and (3) the least-mean-squares (LMS) filter method. In addition there are two new ones: (4) a generalized Kalman filter method and (5) a generalized LMS filter method. The generalized Kalman filter method and the generalized LMS filter method were derived as extensions of the classic methods to permit identification by using more than one measurement per identification cycle. Simulation results are presented for conditions ranging from the ideal case of a stationary transfer matrix and no measurement noise to the more complex cases involving both measurement noise and transfer-matrix variation. Both open-loop identification and closed- loop identification were simulated. Closed-loop mode identification was more challenging than open-loop identification because of the decreasing signal-to-noise ratio as the vibration became reduced. The closed-loop simulation considered both local-model identification, with measured vibration feedback and global-model identification with feedback of the identified uncontrolled vibration. The algorithms were evaluated in terms of their accuracy, stability, convergence properties, computation speeds, and relative ease of implementation.

Jacklin, Stephen A.↗

Adaptive Augmenting Control Flight Characterization Experiment on an F/A-18

This paper summarizes the Adaptive Augmenting Control (AAC) flight characterization experiments performed using an F/A-18 (TN 853). AAC was designed and developed specifically for launch vehicles, and is currently part of the baseline autopilot design for NASA's Space Launch System (SLS). The scope covered here includes a brief overview of the algorithm (covered in more detail elsewhere), motivation and benefits of flight testing, top-level SLS flight test objectives, applicability of the F/A-18 as a platform for testing a launch vehicle control design, test cases designed to fully vet the AAC algorithm, flight test results, and conclusions regarding the functionality of AAC. The AAC algorithm developed at Marshall Space Flight Center is a forward loop gain multiplicative adaptive algorithm that modifies the total attitude control system gain in response to sensed model errors or undesirable parasitic mode resonances. The AAC algorithm provides the capability to improve or decrease performance by balancing attitude tracking with the mitigation of parasitic dynamics, such as control-structure interaction or servo-actuator limit cycles. In the case of the latter, if unmodeled or mismodeled parasitic dynamics are present that would otherwise result in a closed-loop instability or near instability, the adaptive controller decreases the total loop gain to reduce the interaction between these dynamics and the controller. This is in contrast to traditional adaptive control logic, which focuses on improving performance by increasing gain. The computationally simple AAC attitude control algorithm has stability properties that are reconcilable in the context of classical frequency-domain criteria (i.e., gain and phase margin). The algorithm assumes that the baseline attitude control design is well-tuned for a nominal trajectory and is designed to adapt only when necessary. Furthermore, the adaptation is attracted to the nominal design and adapts only on an as-needed basis (see Figure 1). The MSFC algorithm design was formulated during the Constellation Program and reached a high maturity level during SLS through simulation-based development and internal and external analytical review. The AAC algorithm design has three summary-level objectives: (1) "Do no harm;" return to baseline control design when not needed, (2) Increase performance; respond to error in ability of vehicle to track command, and (3) Regain stability; respond to undesirable control-structure interaction or other parasitic dynamics. AAC has been successfully implemented as part of the Space Launch System baseline design, including extensive testing in high-fidelity 6-DOF simulations the details of which are described in [1]. The Dryden Flight Research Center's F/A-18 Full-Scale Advanced Systems Testbed (FAST) platform is used to conduct an algorithm flight characterization experiment intended to fully vet the aforementioned design objectives. FAST was specifically designed with this type of test program in mind. The onboard flight control system has full-authority experiment control of ten aerodynamic effectors and two throttles. It has production and research sensor inputs and pilot engage/disengage and real-time configuration of up to eight different experiments on a single flight. It has failure detection and automatic reversion to fail-safe mode. The F/A-18 aircraft has an experiment envelope cleared for full-authority control and maneuvering and exhibits characteristics for robust recovery from unusual attitudes and configurations aided by the presence of a qualified test pilot. The F/A-18 aircraft has relatively high mass and inertia with exceptional performance; the F/A-18 also has a large thrust-to-weight ratio, owing to its military heritage. This enables the simulation of a portion of the ascent trajectory with a high degree of dynamic similarity to a launch vehicle, and the research flight control system can simulate unstable longitudinal dynamics. Parasitic dynamics such as slosh and bending modes, as well as atmospheric disturbances, are being produced by the airframe via modification of bending filters and the use of secondary control surfaces, including leading and trailing edge flaps, symmetric ailerons, and symmetric rudders. The platform also has the ability to inject signals in flight to simulate structural mode resonances or other challenging dynamics. This platform also offers more test maneuvers and longer maneuver times than a single rocket or missile test, which provides ample opportunity to fully and repeatedly exercise all aspects of the algorithm. Prior to testing on an F/A-18, AAC was the only component of the SLS autopilot design that had not been flight tested. The testing described in this paper raises the Technology Readiness Level (TRL) early in the SLS Program and is able to demonstrate its capabilities and robustness in a flight environment.

VanZwieten, Tannen S.↗

Data Mining for Anomaly Detection

The Vehicle Integrated Prognostics Reasoner (VIPR) program describes methods for enhanced diagnostics as well as a prognostic extension to current state of art Aircraft Diagnostic and Maintenance System (ADMS). VIPR introduced a new anomaly detection function for discovering previously undetected and undocumented situations, where there are clear deviations from nominal behavior. Once a baseline (nominal model of operations) is established, the detection and analysis is split between on-aircraft outlier generation and off-aircraft expert analysis to characterize and classify events that may not have been anticipated by individual system providers. Offline expert analysis is supported by data curation and data mining algorithms that can be applied in the contexts of supervised learning methods and unsupervised learning. In this report, we discuss efficient methods to implement the Kolmogorov complexity measure using compression algorithms, and run a systematic empirical analysis to determine the best compression measure. Our experiments established that the combination of the DZIP compression algorithm and CiDM distance measure provides the best results for capturing relevant properties of time series data encountered in aircraft operations. This combination was used as the basis for developing an unsupervised learning algorithm to define "nominal" flight segments using historical flight segments.

Biswas, Gautam↗

Physical and Dynamical Linkages Between Lightning Jumps and Storm Conceptual Models

The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. Currently, the lightning jump algorithm is being tested in two separate but important efforts. Schultz et al. (2014; this conference) is exploring the transition of the algorithm from its research based formulation to a fully objective algorithm that includes storm tracking, Geostationary Lightning Mapper (GLM) Proxy data and the lightning jump algorithm. Chronis et al. (2014) provides context for the transition to current operational forecasting using lightning mapping array based products. However, what remains is an end-to-end physical and dynamical basis for coupling total lightning flash rates to severe storm manifestation, so the forecaster has a reason beyond simple correlation to utilize the lightning jump algorithm within their severe storm conceptual models. Therefore, the physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relationship to updraft strength, updraft volume, precipitation-sized ice mass, etc.; however, their relationship specifically to lightning jumps is fragmented within the literature. Thus the goal of this study is to use multiple Doppler and polarimetric radar techniques to resolve the physical and dynamical storm characteristics specifically around the time of the lightning jump. This information will help forecasters anticipate lightning jump occurrence, or even be of use to determine future characteristics of a given storm (e.g., development of a mesocyclone, downdraft, or hail signature on radar), providing additional lead time/confidence in the severe storm warning paradigm.

Schultz, Christopher J.↗

A controlled variation scheme for convection treatment in pressure-based algorithm

Convection effect and source terms are two primary sources of difficulties in computing turbulent reacting flows typically encountered in propulsion devices. The present work intends to elucidate the individual as well as the collective roles of convection and source terms in the fluid flow equations, and to devise appropriate treatments and implementations to improve our current capability of predicting such flows. A controlled variation scheme (CVS) has been under development in the context of a pressure-based algorithm, which has the characteristics of adaptively regulating the amount of numerical diffusivity, relative to central difference scheme, according to the variation in local flow field. Both the basic concepts and a pragmatic assessment will be presented to highlight the status of this work.

Shyy, Wei↗

Proceedings of the First NASA Formal Methods Symposium

Topics covered include: Model Checking - My 27-Year Quest to Overcome the State Explosion Problem; Applying Formal Methods to NASA Projects: Transition from Research to Practice; TLA+: Whence, Wherefore, and Whither; Formal Methods Applications in Air Transportation; Theorem Proving in Intel Hardware Design; Building a Formal Model of a Human-Interactive System: Insights into the Integration of Formal Methods and Human Factors Engineering; Model Checking for Autonomic Systems Specified with ASSL; A Game-Theoretic Approach to Branching Time Abstract-Check-Refine Process; Software Model Checking Without Source Code; Generalized Abstract Symbolic Summaries; A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing; Component-Oriented Behavior Extraction for Autonomic System Design; Automated Verification of Design Patterns with LePUS3; A Module Language for Typing by Contracts; From Goal-Oriented Requirements to Event-B Specifications; Introduction of Virtualization Technology to Multi-Process Model Checking; Comparing Techniques for Certified Static Analysis; Towards a Framework for Generating Tests to Satisfy Complex Code Coverage in Java Pathfinder; jFuzz: A Concolic Whitebox Fuzzer for Java; Machine-Checkable Timed CSP; Stochastic Formal Correctness of Numerical Algorithms; Deductive Verification of Cryptographic Software; Coloured Petri Net Refinement Specification and Correctness Proof with Coq; Modeling Guidelines for Code Generation in the Railway Signaling Context; Tactical Synthesis Of Efficient Global Search Algorithms; Towards Co-Engineering Communicating Autonomous Cyber-Physical Systems; and Formal Methods for Automated Diagnosis of Autosub 6000.

Denney, Ewen↗

Contextual classification of multispectral image data - An unbiased estimator for the context distribution

Recent investigations have demonstrated the effectiveness of a contextual classifier that combines spatial and spectral information employing a general statistical approach. This statistical classification algorithm exploits the tendency of certain ground-cover classes to occur more frequently in some spatial contexts than in others. Indeed, a key input to this algorithm is a statistical characterization of the context: the context distribution. Here a discussion is given of an unbiased estimator of the context distribution which, besides having the advantage of statistical unbiasedness, has the additional advantage over other estimation techniques of being amenable to an adaptive implementation in which the context distribution estimate varies according to local contextual information. Results from applying the unbiased estimator to the contextual classification of three real Landsat data sets are presented and contrasted with results from noncontextual classifications and from contextual classifications utilizing other context distribution estimation techniques.

Tilton, J. C.↗

Gaussian maximum likelihood and contextual classification algorithms for multicrop classification

The paper reviews some of the ways in which context has been handled in the remote-sensing literature, and additional possibilities are introduced. The problem of computing exhaustive and normalized class-membership probabilities from the likelihoods provided by the Gaussian maximum likelihood classifier (to be used as initial probability estimates to start relaxation) is discussed. An efficient implementation of probabilistic relaxation is proposed, suiting the needs of actual remote-sensing applications. A modified fuzzy-relaxation algorithm using generalized operations between fuzzy sets is presented. Combined use of the two relaxation algorithms is proposed to exploit context in multispectral classification of remotely sensed data. Results on both one artificially created image and one MSS data set are reported.

Di Zenzo, Silvano↗

Estimation of context for statistical classification of multispectral image data

Recent investigations have demonstrated the effectiveness of a contextual classifier that combines spatial and spectral information employing a general statistical approach. This statistical classification algorithm exploits the tendency of certain ground cover classes to occur more frequently in some spatial contexts than in others. Indeed, a key input to this algorithm is a statistical characterization of the context: the context function. An unbiased estimator of the context function is discussed which, besides having the advantage of statistical unbiasedness, has the additional advantage over other estimation techniques of being amenable to an adaptive implementation in which the context-function estimate varies according to local contextual information. Results from applying the unbiased estimator to the contextual classification of three real Landsat data sets are presented and contrasted with results from noncontextual classifications and from contextual classifications utilizing other context-function estimation techniques.

Tilton, J. C.↗

Survey of new vector computers: The CRAY 1S from CRAY research; the CYBER 205 from CDC and the parallel computer from ICL - architecture and programming

Problems which can arise with vector and parallel computers are discussed in a user oriented context. Emphasis is placed on the algorithms used and the programming techniques adopted. Three recently developed supercomputers are examined and typical application examples are given in CRAY FORTRAN, CYBER 205 FORTRAN and DAP (distributed array processor) FORTRAN. The systems performance is compared. The addition of parts of two N x N arrays is considered. The influence of the architecture on the algorithms and programming language is demonstrated. Numerical analysis of magnetohydrodynamic differential equations by an explicit difference method is illustrated, showing very good results for all three systems. The prognosis for supercomputer development is assessed.

Gentzsch, W.↗