Open AccessBook
Iterative Solution Methods
Reads0
Chats0
TLDR
This paper presents a meta-analyses of matrix eigenvalues and condition numbers for preconditional matrices using the framework of the Perron-Frobenius theory for nonnegative matrices and some simple iterative methods.Abstract:
Preface Acknowledgements 1. Direct solution methods 2. Theory of matrix eigenvalues 3. Positive definite matrices, Schur complements, and generalized eigenvalue problems 4. Reducible and irreducible matrices and the Perron-Frobenius theory for nonnegative matrices 5. Basic iterative methods and their rates of convergence 6. M-matrices, convergent splittings, and the SOR method 7. Incomplete factorization preconditioning methods 8. Approximate matrix inverses and corresponding preconditioning methods 9. Block diagonal and Schur complement preconditionings 10. Estimates of eigenvalues and condition numbers for preconditional matrices 11. Conjugate gradient and Lanczos-type methods 12. Generalized conjugate gradient methods 13. The rate of convergence of the conjugate gradient method Appendices.read more
Citations
More filters
Proceedings ArticleDOI
Gaussian Belief Propagation Solver for Systems of Linear Equations
TL;DR: In this article, a solution based on Gaussian belief propagation (GaBP) is proposed for solving a system of linear equations. But the solution does not involve direct matrix inversion.
Journal ArticleDOI
Numerical study on incomplete orthogonal factorization preconditioners
TL;DR: A class of incomplete orthogonal factorization preconditioners constructed from Givens rotations, incorporating some dropping strategies and updating tricks, are designed, analysed and test for the solution of large sparse systems of linear equations.
Posted Content
Scalable Uplink Signal Detection in C-RANs via Randomized Gaussian Message Passing
TL;DR: This paper endeavors to design a scalable uplink signal detection algorithm, in the sense that both the complexity per unit network area and the total computation time remain constant when the network size grows, and proposes a randomized Gaussian message passing (RGMP) algorithm to improve the convergence.
Proceedings ArticleDOI
Fast GEM wavelet-based image deconvolution algorithm
TL;DR: A new wavelet-based Bayesian approach to image deconvolution, under the space-invariant blur and additive white Gaussian noise assumptions, and a generalized expectation maximization algorithm where the missing variables are the Gaussian modes.
DissertationDOI
Seismic Risk Analysis of Buried Lifelines
TL;DR: In this article, a dreidimensionales numerisches modell entwickelt, in which das dynamische Verhalten von erdverlegten Rohrleitungen beschreibt.