Improved methods and starting values to solve the matrix equations iteratively
Authors:
Ivan G. Ivanov, Vejdi I. Hasanov and Frank Uhlig
Translated by:
Journal:
Math. Comp. 74 (2005), 263278
MSC (2000):
Primary 65F10
Published electronically:
January 27, 2004
MathSciNet review:
2085410
Fulltext PDF Free Access
Abstract 
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Abstract: The two matrix iterations are known to converge linearly to a positive definite solution of the matrix equations , respectively, for known choices of and under certain restrictions on . The convergence for previously suggested starting matrices is generally very slow. This paper explores different initial choices of in both iterations that depend on the extreme singular values of and lead to much more rapid convergence. Further, the paper offers a new algorithm for solving the minus sign equation and explores mixed algorithms that use Newton's method in part.
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Additional Information
Ivan G. Ivanov
Affiliation:
Faculty of Economics and Business Administration, 125 Tzarigradsko chaussee, bl.3, Sofia University, Sofia 1113, Bulgaria
Email:
i_ivanov@feb.unisofia.bg
Vejdi I. Hasanov
Affiliation:
Laboratory of Mathematical Modelling, Shumen University, Shumen 9712, Bulgaria
Email:
v.hasanov@fmi.shubg.net
Frank Uhlig
Affiliation:
Department of Mathematics, Auburn University, Auburn, Alabama 36849–5310
Email:
uhligfd@auburn.edu
DOI:
http://dx.doi.org/10.1090/S0025571804016369
PII:
S 00255718(04)016369
Keywords:
Matrix equation,
positive definite solution,
iterative method,
Newton's method
Received by editor(s):
May 29, 2001
Received by editor(s) in revised form:
May 7, 2003
Published electronically:
January 27, 2004
Additional Notes:
This work is partially supported by Shumen University under Grant #3/04.06.2001.
Article copyright:
© Copyright 2004
American Mathematical Society
