Fortran Package for Least Squares Curve Fitting and the Solution of Simultaneous Equations
Fortran subroutines for least squares curve fitting and solution of simultaneous equations
LINEAR EQUATION↗
SEARCH · Search NASA
Results for “least squares solution”
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.
Least-squares finite element solutions for three-dimensional backward-facing step flow
Comprehensive numerical solutions of the steady state incompressible viscous flow over a three-dimensional backward-facing step up to Re equals 800 are presented. The results are obtained by the least-squares finite element method (LSFEM) which is based on the velocity-pressure-vorticity formulation. The computed model is of the same size as that of Armaly's experiment. Three-dimensional phenomena are observed even at low Reynolds number. The calculated values of the primary reattachment length are in good agreement with experimental results.
Jiang, Bo-Nan↗
Least-squares finite element solution of 3D incompressible Navier-Stokes problems
Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.
Jiang, Bo-Nan↗
On damping mechanisms in beams
A partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite. Four separate damping mechanisms consisting of air damping, strain rate damping, spatial hysteresis and time hysteresis are considered experimentally. Dynamic tests were performed to produce time histories. The time history data is then used along with an approximate model to form a sequence of least squares problems. The solution of the least squares problem yields the estimated damping coefficients. The resulting experimentally determined analytical model is compared with the time histories via numerical simulation of the dynamic response. The procedure suggested here is compared with a standard modal damping ratio model commonly used in experimental modal analysis.
Banks, H. T.↗
On damping mechanisms in beams
A partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite. Four separate damping mechanisms consisting of air damping, strain rate damping, spatial hysteresis and time hysteresis are considered experimentally. Dynamic tests were performed to produce time histories. The time history data is then used along with an approximate model to form a sequence of least squares problems. The solution of the least squares problem yields the estimated damping coefficients. The resulting experimentally determined analytical model is compared with the time histories via numerical simulation of the dynamic response. The procedure suggested here is compared with a standard modal damping ratio model commonly used in experimental modal analysis.
Banks, H. T.↗
Least-Squares Spectral Element Solutions to the CAA Workshop Benchmark Problems
This paper presents computed results for some of the CAA benchmark problems via the acoustic solver developed at Rocketdyne CFD Technology Center under the corporate agreement between Boeing North American, Inc. and NASA for the Aerospace Industry Technology Program. The calculations are considered as benchmark testing of the functionality, accuracy, and performance of the solver. Results of these computations demonstrate that the solver is capable of solving the propagation of aeroacoustic signals. Testing of sound generation and on more realistic problems is now pursued for the industrial applications of this solver. Numerical calculations were performed for the second problem of Category 1 of the current workshop problems for an acoustic pulse scattered from a rigid circular cylinder, and for two of the first CAA workshop problems, i. e., the first problem of Category 1 for the propagation of a linear wave and the first problem of Category 4 for an acoustic pulse reflected from a rigid wall in a uniform flow of Mach 0.5. The aim for including the last two problems in this workshop is to test the effectiveness of some boundary conditions set up in the solver. Numerical results of the last two benchmark problems have been compared with their corresponding exact solutions and the comparisons are excellent. This demonstrates the high fidelity of the solver in handling wave propagation problems. This feature lends the method quite attractive in developing a computational acoustic solver for calculating the aero/hydrodynamic noise in a violent flow environment.
Lin, Wen H.↗
An application of least squares method to the solution of the inverse problem of heat conduction.
Heat input to a body surface, using least squares method
THERMAL CONDUCTOR↗
Iterative methods for solving nonlinear least squares problems
Iterative methods for solving nonlinear least squares problems
ITERATIVE SOLUTION↗
ORACLS: A system for linear-quadratic-Gaussian control law design
A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.
Armstrong, E. S.↗
A least-squares procedure for the solution of the lifting-line integral equation
Explore the source record for details and available documents.
LIFT DISTRIBUTION, WING-SPAN↗
Shuttle onboard IMU alignment methods
The current approach to the shuttle IMU alignment is based solely on the Apollo Deterministic Method. This method is simple, fast, reliable and provides an accurate estimate for the present cluster to mean of 1,950 transformation matrix. If four or more star sightings are available, the application of least squares analysis can be utilized. The least squares method offers the next level of sophistication to the IMU alignment solution. The least squares method studied shows that a more accurate estimate for the misalignment angles is computed, and the IMU drift rates are a free by-product of the analysis. Core storage requirements are considerably more; estimated 20 to 30 times the core required for the Apollo Deterministic Method. The least squares method offers an intermediate solution utilizing as much data that is available without a complete statistical analysis as in Kalman filtering.
Henderson, D. M.↗
The covariance matrix for the solution vector of an equality-constrained least-squares problem
Methods are given for computing the covariance matrix for the solution vector of an equality-constrained least squares problem. The methods are matched to the solution algorithms given in the book, 'Solving Least Squares Problems.'
Lawson, C. L.↗
Solution of an integral equation encountered in studies on radiative transfer in completely absorbing leaf canopies
The leaf normal distribution function is related to the extinction coefficient of direct solar radiation by a Fredholm integral equation of the first kind. The integral equation is solved by the method of constrained least squares. The solutions are stable and correct only in extreme cases and, in general, it is not possible to recover an arbitrary leaf normal distribution function.
Myneni, Ranga B.↗
Robust and optimal alignment of high-dimensional data using maximum likelihood estimation through a random sample consensus framework
Abstract Correcting spatial orientations of groups of high-dimensional data sets such that they are all in a consistent coordinate system is often a time-consuming and error-prone process. Automation of this process can be accomplished by using Generalized Procrustes Analysis to estimate the relative orientations among a population of high-dimensional data sets. A least squares Procrustes solution is applied through a maximum likelihood estimation and random sample consensus framework for robustness. The likelihood model is comprised of a mixture distribution where inliers are modeled using t -distribution and outliers from a uniform distribution. Applications will focus on a synthetic data set that emulates triaxial acceleration data and also real shock data from a population of triaxial accelerometers. Outliers represent either non-rigid body responses, environmental noise, and/or sensor and data acquisition issues. The intended application for the methodology is to robustly automate the rotation of populations of experimentally collected triaxial accelerometer data sets to a single global coordinate system.
LOSAC↗
Applications of a mathematical programming technique to finite thrust rocket trajectory optimization
Iterative solution of least squares programming problem for finite thrust rocket trajectory optimization
Armstrong, E. S.↗
Weighted least squares formulas for multiple Doppler radar analysis
An algorithm is developed for the analysis of multiple Doppler radar data in meteorological applications. The algorithm is based on the least squares linear solutions for the variable parameters of a local particle velocity field. The computational sequence for the algorithm is described, and some factors influencing the covariance of Doppler measurement errors are discussed.
Wilson, F. W., Jr.↗
Determination of relative site motions in the western United States using Mark III very long baseline interferometry
Four years of very long baseline interferometry (VLBI) measurements involving fixed and mobile stations in the western U.S. are analyzed using weighted least squares. Baseline solution time series are used to estimate rates of change of the vector baseline between pairs of VLBI stations. Horizontal vector motions are determined for 18 sites with respect to a site in the Mojave desert. Six sites west of and two sites just to the east of the San Andreas fault show northwestward motion closely parallel to the San Andreas fault. Their motions range from 18 to 43 mm/yr and are significant at confidence levels greater than 99 percent. Motions in California relative to interior North American plate sites are used to estimate an integrated contribution from Basin and Range spreading to the total relative Pacific plate motion as 9-10 mm/yr. A maximum relative velocity of 50-51 mm/yr is found between the interior North American sites and the western California sites, in close agreement with the NUVEL-1 plate motion model.
Clark, T. A.↗
An analysis of the Voyager 2 Ultraviolet Spectrometer occultation data at Uranus - Inferring heat sources and model atmospheres
Heat source information is derived here from the Voyager 2 Ultraviolet Spectrometer occultation data of Uranus. Analytic functions for the local heat dependence on altitude are used to obtain a temperature profile by solving the heat equation. The stellar entrance and exit occultation and a solar occultation are used to infer the thermal and density structure of the atmosphere. The least squares fit solution to the solar occultation data gives one source located at 1.8 x 10 exp -5 microbar with a strength of 0.056 +/- 0.01 erg/sq cm/s. Latitudinal temperature gradients are obtained.
Stevens, Michael H.↗