Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
HTML articles powered by AMS MathViewer

by Ivan G. Ivanov, Vejdi I. Hasanov and Frank Uhlig PDF
Math. Comp. 74 (2005), 263-278 Request permission


The two matrix iterations $X_{k+1}=I\mp A^*X_k^{-1}A$ are known to converge linearly to a positive definite solution of the matrix equations $X\pm A^*X^{-1}A=I$, respectively, for known choices of $X_0$ and under certain restrictions on $A$. The convergence for previously suggested starting matrices $X_0$ is generally very slow. This paper explores different initial choices of $X_0$ in both iterations that depend on the extreme singular values of $A$ 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 Newtonโ€™s method in part.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2000): 65F10
  • Retrieve articles in all journals with MSC (2000): 65F10
Additional Information
  • Ivan G. Ivanov
  • Affiliation: Faculty of Economics and Business Administration, 125 Tzarigradsko chaussee, bl.3, Sofia University, Sofia 1113, Bulgaria
  • Email:
  • Vejdi I. Hasanov
  • Affiliation: Laboratory of Mathematical Modelling, Shumen University, Shumen 9712, Bulgaria
  • Email:
  • Frank Uhlig
  • Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849โ€“5310
  • Email:
  • 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.
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 263-278
  • MSC (2000): Primary 65F10
  • DOI:
  • MathSciNet review: 2085410