Showing papers on "Singular value decomposition published in 1973"

Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems

Abstract: This paper describes a technique for obtaining error bounds for certain characteristic subspaces associated with the algebraic eigenvalue problem, the generalized eigenvalue problem, and the singular value decomposition. The method also gives perturbation bounds for isolated eigenvalues and useful information about clusters of eigenvalues. The bounds are obtained from an iterative process for generating the subspaces in question, and one or more steps of the iteration can be used to construct perturbation estimates whose error can be bounded.

On the Numerical Solution of Ill-Conditioned Linear Systems with Applications to Ill-Posed Problems

Abstract: We consider the solution of ill-conditioned linear systems using the singular value decomposition, and show how this can improve the accuracy of the computed solution for certain kinds of right-hand sides Then we indicate how this technique is especially appropriate for some classical ill-posed problems of mathematical physics

On the almost rank deficient case of the least squares problem

Abstract: This paper studies properties of the solutions to overdetermined systems of linear equations whose matrices are almost rank deficient. Let such a system be approximated by the system of rankr which is closest in the euclidean matrix norm. The residual of the approximate solution depends on the scaling of the independent variable. Sharp bounds are given for the sensitivity of the residual to the scaling of the independent variable. It turns out that these bounds depend critically on a few factors which can be computed in connection with the singular value decomposition. Further the influence from the scaling on the pseudo-inverse solution of a rank deficient system is estimated.

Numerical image restoration by the method of singular-value decomposition

Abstract: BS>From seventh international conference on system sciences; Honolulu, Hawaii, USA (8 Jan 1974). The numerical image restoration problem is considered for the case of shift-variant imaging. The solution formalism presented is based on the method of singular-value decomposition. Some special-case versions of the formalism are considered. (auth)