Journal ArticleDOI
Analysis of the Diagonal Pivoting Method
TLDR
In this paper, a backward error analysis of the diagonal pivoting method for solving symmetric systems of linear equations is presented, which shows that the elements of the associated error matrix can be bounded in time.Abstract:
A backwards error analysis of the diagonal pivoting method for solving symmetric (indefinite) systems of linear equations shows that the elements of the associated error matrix can be bounded in te...read more
Citations
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Journal ArticleDOI
Computational methods of linear algebra
D. K. Faddeev,V. N. Faddeeva +1 more
TL;DR: A survey of computational methods in linear algebra can be found in this article, where the authors discuss the means and methods of estimating the quality of numerical solution of computational problems, the generalized inverse of a matrix, the solution of systems with rectangular and poorly conditioned matrices, and more traditional questions such as algebraic eigenvalue problems and systems with a square matrix.
Book
Matrix algorithms
TL;DR: This volume treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them.
Journal ArticleDOI
Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations
TL;DR: Methods for solving symmetric indefinite systems are surveyed including a new one which is stable and almost as fast as the Cholesky method.
Journal ArticleDOI
Some stable methods for calculating inertia and solving symmetric linear systems
James R. Bunch,Linda Kaufman +1 more
TL;DR: Several decompositions of symmetry matrices for calculating inertia and solving systems of linear equations are discussed and new partial pivoting strategies for decomposing symmetric matrices are introduced and analyzed.
Journal ArticleDOI
A survey of sparse matrix research
TL;DR: This paper surveys the state of the art in sparse matrix research in January 1976, and discusses the solution of sparse simultaneous linear equations, including the storage of such matrices and the effect of paging on sparse matrix algorithms.
References
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Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Journal ArticleDOI
Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations
TL;DR: Methods for solving symmetric indefinite systems are surveyed including a new one which is stable and almost as fast as the Cholesky method.
Journal ArticleDOI
Error Analysis of Direct Methods of Matrix Inversion
TL;DR: This paper determines error bounds for a number of the most effective direct methods of inverting a matrix by analyzing the effect of the rounding errors made in the solution of the equations.
Journal ArticleDOI
Equilibration of Symmetric Matrices in the Max-Norm
TL;DR: A simple noni te ra t ive a lgor i thm which equi l ibrates any symmetr ic mat r ix (with no null rows) in the max-norm is presented and analyzed.
Related Papers (5)
Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations
Some stable methods for calculating inertia and solving symmetric linear systems
James R. Bunch,Linda Kaufman +1 more