Journal ArticleDOI
Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
G. Peters,James Hardy Wilkinson +1 more
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Inverse iteration is one of the most widely used algorithms in practical linear algebra as discussed by the authors, but an understanding of its main numerical properties has developed piecemeal over the last thirty years: a m...Abstract:
Inverse iteration is one of the most widely used algorithms in practical linear algebra but an understanding of its main numerical properties has developed piecemeal over the last thirty years: a m...read more
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Book
Optimization Algorithms on Matrix Manifolds
TL;DR: Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis and will be of interest to applied mathematicians, engineers, and computer scientists.
Book
Iterative Methods for Linear and Nonlinear Equations
TL;DR: Preface How to Get the Software How to get the Software Part I.
Journal ArticleDOI
The Quadratic Eigenvalue Problem
TL;DR: This work surveys the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques.
Book
Introduction to Numerical Continuation Methods
Eugene L. Allgower,Kurt Georg +1 more
TL;DR: The Numerical Continuation Methods for Nonlinear Systems of Equations (NCME) as discussed by the authors is an excellent introduction to numerical continuuation methods for solving nonlinear systems of equations.
References
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Journal ArticleDOI
Convergence of the newton process to multiple solutions
TL;DR: Schroder as discussed by the authors showed that the convergence of the Newton process of successive approximations to a multiple solution of a scalar equation was geometric in character, and that quadratic convergence could be restored by multiplying the ordinary corrections by a constant.
Journal ArticleDOI
The solution of characteristic value-vector problems by Newton's method
P. M. Anselone,L. B. Rall +1 more
TL;DR: In this article, the characteristic value-vector problem is formulated as a nonlinear problem in a Banach space, and the continuous dependence on T of characteristic values and vectors is investigated.
Journal ArticleDOI
Computing Invariant Subspaces of a General Matrix when the Eigensystem is Poorly Conditioned
TL;DR: This paper defines a class of matrices where this is true, and proposes a technique for calculating bases for these invariant subspaces, and shows that for this class the technique provides basis vectors which are accurate and span the subspaced well.
Journal ArticleDOI
Rigorous machine bounds for the eigensystem of a general complex matrix
TL;DR: The technique is outlined in general terms and it is shown that the bounds can be found in terms of computed quantities if ll-Elloo = ||/ — XFU«, < 1, where X is the matrix of approximate eigenvectors and Y is an approximate inverse for X.