Using the Frechet derivative to improve Arnoldi's method

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" Using the Frechet derivative to improve Arnoldi's method "
H.-A. Sun M. Saleem

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1113436
Doc. No	:	TLpq304598929
Main Entry	:	H.-A. Sun
	:	M. Saleem
Title & Author	:	Using the Frechet derivative to improve Arnoldi's method\ H.-A. SunM. Saleem
College	:	San Jose State University
Date	:	1999
student score	:	1999
Degree	:	M.S.
Page No	:	67
Abstract	:	One recently developed Krylov method for solving linear systems is Arnoldi's method. Arnoldi's method is an orthogonal projection method onto a Krylov subspace Km for general non-Hermitian matrices (16). In this thesis, the method is applied to ill-conditioned and non-symmetric matrices. The results in this thesis suggest that the choice of the initial guess plays an important role in deciding how Arnoldi's method will converge or when Arnoldi's method will converge by using the Frechet derivative. In this thesis, the Frechet derivative is a tool to find the best possible initial guess of linear systems of equations for Arnoldi's method. Also, the thesis compares convergence with 3 different algorithms including Arnoldi's method, Arnoldi's method improved by the Frechet derivative, and Matlab's "backslash" method.
Subject	:	Applied sciences
	:	Computer science
	:	Mathematics
	:	Mathematics
	:	Pure sciences