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.


A look-ahead Lánczos algorithm for unsymmetric matrices
HTML articles powered by AMS MathViewer

by Beresford N. Parlett, Derek R. Taylor and Zhishun A. Liu PDF
Math. Comp. 44 (1985), 105-124 Request permission


The two-sided Lanczos algorithm sometimes suffers from serious breakdowns. These occur when the associated moment matrix does not permit triangular factorization. We modify the algorithm slightly so that it corresponds to using a $2 \times 2$ pivot in triangular factorization whenever a $1 \times 1$ pivot would be dangerous. The likelihood of breakdown is greatly reduced. The price paid is that the tridiagonal matrix produced by the algorithm now has bumps whenever a $2 \times 2$ pivot is used. Experiments with several versions of the algorithm on a variety of matrices are described, including some large problems arising in the study of plasma instability.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65F15
  • Retrieve articles in all journals with MSC: 65F15
Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Math. Comp. 44 (1985), 105-124
  • MSC: Primary 65F15
  • DOI:
  • MathSciNet review: 771034