Showing papers on "Singular value decomposition published in 1981"

A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix

Abstract: We present a block Lanczos method to compute the largest singular values and corresponding left and right singular vectors of a large sparse matrix. Our algorithm does not transform the matrix A but accesses it only through a user-supplied routine which computes AX or $A^t$X for a given matrix X. This paper also includes a thorough discussion of the various ways to compute the singular value decomposition of a banded upper triangular matrix; this problem arises as a subproblem to be solved during the block Lanczos procedure.

Analysis of Measurements Based on the Singular Value Decomposition

Abstract: The problem of maintaining quality control of manufactured parts is considered This involves matching points on the parts with corresponding points on a drawing The difficulty in this process is that the measurements are often in different coordinate systems Using the assumption that the relation between the two sets of coordinates is a certain rigid transformation, an explicit least squares solution is obtained This solution requires the singular value decomposition of a related matrixOther topics in the paper include an appropriate angular representation of the resulting orthogonal transformation matrix, and a computational algorithm for the various required quantities

SVD pseudoinversion image reconstruction

Abstract: The singular value decomposition (SVD) pseudoinversion method has been applied to image reconstruction from projections. In this paper, two SVD pseudoinversion methods are discussed in the search for optimum restoration; one uses Wiener filtering and the other uses truncated inverse filtering. These methods partly overcome the ill-conditioned nature of reconstruction problems by trading off between noise and signal quality. Using computer simulation, the present SVD method was compared with the conventional Fourier convolution method. Results are presented together with some limitations peculiar to the application of this method for image reconstruction and restoration.

Biennial Variations in Surface Temperature over the United States as Revealed by Singular Decomposition

Abstract: Surface temperature variations over the contiguous United States during the period 1931–75 are examined using mean monthly averages for the 344 climate divisions. This data matrix is decomposed into orthogonal components using the method of singular decomposition. The third empirical orthogonal function, which accounts for nine percent of the nonseasonal variance, exhibits a significant quasi-biennial oscillation (QBO). The phase and amplitude of the QBO implied by this analysis were further studied using an extension of the singular decomposition method which we call Hilbert Singular Decomposition (USD). HSD uses the Hilbert Transformer to augment the data matrix and transform the real elements into complex elements so that coherent “wavelike” variations can be represented in terms of a complex singular decomposition. Additional cross-spectral analyses were performed for selected climate division aggregates. Two areas of maximum QBO amplitude are indicated; one over the northeastern United State...

Geometric methods for determining system poles from transient response

Abstract: The problem treated is that of identifying the poles of a finite order system by observing its transient decay after cessation of input, for a limited time, using (possibly) multiple observation points and experimental repetition. Various approaches are studied, having the common characteristic that a homogeneous matrix equation must be solved. Several techniques that have been given scant attention in the literature are consolidated by a geometric treatment, together with new results including an analytical treatment of the consequences of assuming an excessively high system order, derivation of a statistically unbiased estimate for an intermediate parameter in the solution, new theorems on error effects, a recipe for effective use of the singular value decomposition, and a new method for suppression of extraneous poles.

A singular value decomposition for the radon transform in n-dimensional euclidean space

Abstract: We construct the singular value decomposition of the Radon transform when the Radon transform is restricted to functions which are either square integrable on the unit disc in IR n with respect to one of the weights (1-r 2)n/2-λ: or square integrable on IR n with respect to exp(r 2). An application to calculating mollifiers for approximate inversion of the sampled Radon transform is discussed.

Singular value decomposition and spectral analysis

Abstract: Linear-Prediction-based (LP) methods for fitting multiple-sinusoid signal models to observed data, such as the forward-backward (FBLP) method of Nuttall (5) and Ulrych and Clayton (6), are very ill-conditioned. The locations of estimated spectral peaks can be greatly affected by a small amount of additive noise. LP estimation of frequencies can be greatly improved by singular value decomposition of the LP data matrix. The improved performance of the resulting new technique, which we called the principal eigenvector method (13, 14) is demonstrated by using it on one and two dimensional data.

Singular value analysis of deformable systems

Abstract: Singular value analysis, balancing, and approximation of a class of deformable systems are investigated. The deformable systems considered herein include several important cases of flexible aerospace vehicles and are characterized by countably infinitely many poles and zeros on the imaginary axis. The analysis relies completely on the so-called asymptotic singular value decomposition of the Hankel operator associated with the impulse response of the system. A parametric study of a six-dimensional single-input single-output case is performed.

On the relationships between unbounded asymptote behaviour of multivariable root loci, impulse response and infinite zeros

Abstract: Using singular value decomposition techniques, and making systematic use of the Schur complement for a partitioned matrix, an investigation is carried out of how the input and output spaces associated with a square transfer matrix can be decomposed in terms of the way in which a system responds to vector impulses of various orders. The results so obtained are then used to characterise the forms of the behaviour of the unbounded asymptotes of the multivariable root locus. A discussion is given of the asymptotes and infinite zeros.

Analysis of experimental curves using singular value decomposition

Abstract: This paper describes a singular value decomposition (SVD) technique for the analysis of experimental response curves. The SVD of a set of curves shows that curves can be decomposed to become a linear combination of some intrinsic-component patterns. The interpolation of curves can then be reduced to a simple interpolation of weighting coefficients. The SVD method is applied to an estimation problem of γ-ray response spectra, and a library of the response curves is constructed.

Stability investigations of various representations of the gravity field

Abstract: A number of problems in physical geodesy are improperly posed in the sense that the approximate solution is not continuously dependent on the given observations. A transformation of the minimum norm least squares estimates for different types of gravity representations to the spectral domain, via a singular value decomposition, allows an easy insight into the stability situation of these representations. For the density layer or point mass model, Bjerhammar’s method, and the least squares collocation model the filter expressions are derived which control their stability. It is shown in which way the shape of the filters is influenced by the a priori variance of the measurement noise, the choice of the radius of the Bjerhammar sphere, and the degree variance model.

A numerical inversion scheme for geoelectrical soundings

Abstract: A simple numerical inversion scheme for estimatingn-layer model parameters from observed geoelectrical resistivity data can be used in either the space or wavenumber domain. The technique utilizes Madden's Transmission Line Analogy to compute the resistivity transforms and linear filter theory to accomplish the excursions between the space and wavenumber domains. The inversion is effected by an iterative refinement scheme employing the stochastic inverse which is approximate to the generalized inverse. No singular decomposition analysis is required and the scheme is stable under ill conditions. The inversion scheme not only gives the desired estimates; it exposes redundant parameters and irrelevant data and is easily programmed on a desk-top mini computer. Examples of inverse modeling with hypothetical and field data are discussed.

For control system design

Abstract: The concept of suboptimality is applied totesting validity of reduced-order models in design of feedback schemes for large-scale systems. Aggregation and singular value decomposition as model reduction techniques, are interpreted in the expansioncontraction framework, which is suitable for evaluation of suboptimality of closed-loop systems resulting from reduced order designs. The proposed validation procedure is applied to a control design of a large space structure.

An algorithm for computing singular values of large matrices for use in the analysis of large systems

Abstract: An algorithm for computing a few or many of the singular values (and a few of the corresponding singular vectors) of large matrices is presented. If the matrices under consideration are sparse, then this procedure has storage requirements that increase only linearly with the order of the matrix. Such an algorithm may prove useful in sensitivity and stability analyses of very large systems.