SEARCH · Search NASA

Results for “column pivoting”

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.

SourceResearch connectionFrom yearThrough year

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

13 records

All sources NASA NTRS DOE OSTI

NASA NTRS1990

Applications of truncated QR methods to sinusoidal frequency estimation

Three truncated QR methods are proposed for sinusoidal frequency estimation: (1) truncated QR without column pivoting (TQR), (2) truncated QR with preordered columns, and (3) truncated QR with column pivoting. It is demonstrated that the benefit of truncated SVD for high frequency resolution is achievable under the truncated QR approach with much lower computational cost. Other attractive features of the proposed methods include the ease of updating, which is difficult for the SVD method, and numerical stability. TQR methods thus offer efficient ways to identify sinusoidals closely clustered in frequencies under stationary and nonstationary conditions.

Hsieh, S. F.↗

NASA NTRS1991

Algorithm For Solution Of Subset-Regression Problems

Reliable and flexible algorithm for solution of subset-regression problem performs QR decomposition with new column-pivoting strategy, enables selection of subset directly from originally defined regression parameters. This feature, in combination with number of extensions, makes algorithm very flexible for use in analysis of subset-regression problems in which parameters have physical meanings. Also extended to enable joint processing of columns contaminated by noise with those free of noise, without using scaling techniques.

Verhaegen, Michel↗

NASA NTRS1985

Mechanical features of the shuttle rotating service structure

With the development of the space shuttle launching facilities, it became mandatory to develop a shuttle rotating service structure to provide for the insertion and/or removal of payloads at the launch pads. The rotating service structure is a welded tubular steel space frame 189 feet high, 65 feet wide, and weighing 2100 tons. At the pivot column the structure is supported on a 30 inch diameter hemispherical bearing. At the opposite terminus the structure is supported on two truck assemblies each having eight 36 inch diameter double flanged wheels. The following features of the rotating service structure are discussed: (1) thermal expansion and contraction; (2) hurricane tie downs; (3) payload changeout room; (4) payload ground handling mechanism; (5) payload and orbiter access platforms; and (6) orbiter cargo bay access.

Crump, J. M.↗

NASA NTRS1987

On the reliable and flexible solution of practical subset regression problems

A new algorithm for solving subset regression problems is described. The algorithm performs a QR decomposition with a new column-pivoting strategy, which permits subset selection directly from the originally defined regression parameters. This, in combination with a number of extensions of the new technique, makes the method a very flexible tool for analyzing subset regression problems in which the parameters have a physical meaning.

Verhaegen, M. H.↗

NASA NTRS1987

The minimal residual QR-factorization algorithm for reliably solving subset regression problems

A new algorithm to solve test subset regression problems is described, called the minimal residual QR factorization algorithm (MRQR). This scheme performs a QR factorization with a new column pivoting strategy. Basically, this strategy is based on the change in the residual of the least squares problem. Furthermore, it is demonstrated that this basic scheme might be extended in a numerically efficient way to combine the advantages of existing numerical procedures, such as the singular value decomposition, with those of more classical statistical procedures, such as stepwise regression. This extension is presented as an advisory expert system that guides the user in solving the subset regression problem. The advantages of the new procedure are highlighted by a numerical example.

Verhaegen, M. H.↗

NASA NTRS1987

The use of the QR factorization in the partial realization problem

The use of the QR factorization of the Hankel matrix in solving the partial realization problem is analyzed. Straightforward use of the QR factorization results in a realization scheme that possesses all of the computational advantages of Rissanen's realization scheme. These latter properties are computational efficiency, recursiveness, use of limited computer memory, and the realization of a system triplet having a condensed structure. Moreover, this scheme is robust when the order of the system corresponds to the rank of the Hankel matrix. When this latter condition is violated, an approximate realization could be determined via the QR factorization. In this second scheme, the given Hankel matrix is approximated by a low-rank non-Hankel matrix. Furthermore, it is demonstrated that column pivoting might be incorporated in this second scheme. The results presented are derived for a single input/single output system, but this does not seem to be a restriction.

Verhaegen, M. H.↗

NASA NTRS1987

On the reliable and flexible solution of practical subset regression problems

Verhaegen, M.↗

NASA NTRS1982

Motion systems providing three or four degrees of freedom

A motion system is provided by a platform generally parallel to a base and connected thereto by a column and powered and controlled extensible members, at least three of which are connected between distributed points around the column. In a three degree of freedom device, the column is conical, rigidly supported at its base with a universal joint at its top. The points of attachment define triangles in the base and in the platform surrounding the column with one extensible member connected between each. In the four degree of freedom version, the column is modified by making it effectively a column which is pivoted or guided at the base or contains an extensible member, preferably retains its triangular shape and its universal joint connection to the platform at its apex. For stability four powered and controlled extensible members are provided between points in the base and platform distributed around the column, a preferred pattern of arrangement being a square with the column at the center.

Chou, Richard C.↗

NASA NTRS2023

The Polarimetric Radar Scattering Properties of Oriented Aggregates

The scattering properties of aggregates are studied herein. Early aggregates (<7 monomers) of branched planar crystals and mature aggregates (up to 100 monomers) of columns are randomly generated with varying assumptions about the monomer attachment processes and the orientation behavior during collection. The resulting physical properties of the aggregates correspond well with prior in situ and retrieved sizes and shapes. Assumed azimuthally uniform orientations during collection and monomer pivoting upon attachment resulted in flatter and denser aggregates. The column aggregates had lower density and more spherical shapes than the branched planar crystal aggregates. The scattering properties were calculated using the discrete dipole approximation for a set of orientation angles and transformed to spectral coefficients representing modes of orientation angle variability. The zeroth- and second-order coefficients dominate this variability, with the zeroth-order coefficients representing the scattering properties for randomly oriented particles. The second-order coefficients for backscatter showed differences between horizontal and vertical polarization increasing with density, and these coefficients for specific differential phase increase with both mass and density. Similarly, coefficients for the copolar covariance decreased with density. Rapid changes in the contributions to the radar moments from the second-order coefficients from low to moderate density were observed, likely due to the increasing presence of horizontally aligned monomers in the aggregate structure. Differences in how differential reflectivity and correlation coefficient evolve with the orientation distribution parameters suggest that these measurements, along with specific differential phase and reflectivity, provide complementary information about aggregate sizes, shapes, and orientation distributions.

Cloud microphysics↗

NASA NTRS1992

Block LU factorization

Many of the currently popular 'block algorithms' are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by columns. Moreover, for a general matrix the level of instability in block LU factorization can be founded in terms of the condition number kappa(A) and the growth factor for Gaussian elimination without pivoting. A consequence is that block LU factorization is stable for a matrix A that is symmetric positive definite or point diagonally dominant by rows or columns as long as A is well-conditioned.

Demmel, James W.↗

NASA NTRS1984

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

David, R. E.↗

NASA NTRS2013

Long-Term Variability of AGN at Hard X-Rays

Variability at all observed wavelengths is a distinctive property of active galactic nuclei (AGN). Hard X-rays provide us with a view of the innermost regions of AGN, mostly unbiased by absorption along the line of sight. Characterizing the intrinsic hard X-ray variability of a large AGN sample and comparing it to the results obtained at lower X-ray energies can significantly contribute to our understanding of the mechanisms underlying the high-energy radiation. Methods. Swift/BAT provides us with the unique opportunity to follow, on time scales of days to years and with a regular sampling, the 14-195 keV emission of the largest AGN sample available up to date for this kind of investigation. As a continuation of an early work on the first 9 months of BAT data, we study the amplitude of the variations, and their dependence on sub-class and on energy, for a sample of 110 radio quiet and radio loud AGN selected from the BAT 58-month survey. About 80 of the AGN in the sample are found to exhibit significant variability on months to years time scales, radio loud sources being the most variable. The amplitude of the variations and their energy dependence are incompatible with variability being driven at hard X-rays by changes of the absorption column density. In general, the variations in the 14-24 and 35-100 keV bands are well correlated, suggesting a common origin of the variability across the BAT energy band. However, radio quiet AGN display on average 10 larger variations at 14-24 keV than at 35-100 keV and a softer-when-brighter behavior for most of the Seyfert galaxies with detectable spectral variability on month time scale. In addition, sources with harder spectra are found to be more variable than softer ones. These properties are generally consistent with a variable power law continuum, in flux and shape, pivoting at energies 50 keV, to which a constant reflection component is superposed. When the same time scales are considered, the timing properties of AGN at hard X-rays are comparable to those at lower energies, with at least some of the differences possibly ascribable to components contributing differently in the two energy domains (e.g., reflection, absorption).

X-rays↗

NASA NTRS1990

Cassini atmospheric chemistry mapper. Volume 1. Investigation and technical plan

The Cassini Atmospheric Chemistry Mapper (ACM) enables a broad range of atmospheric science investigations for Saturn and Titan by providing high spectral and spatial resolution mapping and occultation capabilities at 3 and 5 microns. ACM can directly address the major atmospheric science objectives for Saturn and for Titan, as defined by the Announcement of Opportunity, with pivotal diagnostic measurements not accessible to any other proposed Cassini instrument. ACM determines mixing ratios for atmospheric molecules from spectral line profiles for an important and extensive volume of the atmosphere of Saturn (and Jupiter). Spatial and vertical profiles of disequilibrium species abundances define Saturn's deep atmosphere, its chemistry, and its vertical transport phenomena. ACM spectral maps provide a unique means to interpret atmospheric conditions in the deep (approximately 1000 bar) atmosphere of Saturn. Deep chemistry and vertical transport is inferred from the vertical and horizontal distribution of a series of disequilibrium species. Solar occultations provide a method to bridge the altitude range in Saturn's (and Titan's) atmosphere that is not accessible to radio science, thermal infrared, and UV spectroscopy with temperature measurements to plus or minus 2K from the analysis of molecular line ratios and to attain an high sensitivity for low-abundance chemical species in the very large column densities that may be achieved during occultations for Saturn. For Titan, ACM solar occultations yield very well resolved (1/6 scale height) vertical mixing ratios column abundances for atmospheric molecular constituents. Occultations also provide for detecting abundant species very high in the upper atmosphere, while at greater depths, detecting the isotopes of C and O, constraining the production mechanisms, and/or sources for the above species. ACM measures the vertical and horizontal distribution of aerosols via their opacity at 3 microns and, particularly, at 5 microns. ACM recovers spatially-resolved atmospheric temperatures in Titan's troposphere via 3- and 5-microns spectral transitions. Together, the mixing ratio profiles and the aerosol distributions are utilized to investigate the photochemistry of the stratosphere and consequent formation processes for aerosols. Finally, ring opacities, observed during solar occultations and in reflected sunlight, provide a measurement of the particle size and distribution of ring material. ACM will be the first high spectral resolution mapping spectrometer on an outer planet mission for atmospheric studies while retaining a high resolution spatial mapping capability. ACM, thus, opens an entirely new range of orbital scientific studies of the origin, physio-chemical evolution and structure of the Saturn and Titan atmospheres. ACM provides high angular resolution spectral maps, viewing nadir and near-limb thermal radiation and reflected sunlight; sounds planetary limbs, spatially resolving vertical profiles to several atmospheric scale heights; and measures solar occultations, mapping both atmospheres and rings. ACM's high spectral and spatial resolution mapping capability is achieved with a simplified Fourier Transform spectrometer with a no-moving parts, physically compact design. ACM's simplicity guarantees an inherent stability essential for reliable performance throughout the lengthy Cassini Orbiter mission.

Smith, William Hayden↗