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.


On the convergence rates of variational methods. I. Asymptotically diagonal systems
HTML articles powered by AMS MathViewer

by L. M. Delves and K. O. Mead PDF
Math. Comp. 25 (1971), 699-716 Request permission


We consider the problem of estimating the convergence rate of a variational solution to an inhomogeneous equation. This problem is not soluble in general without imposing conditions on both the class of expansion functions and the class of problems considered; we introduce the concept of “asymptotically diagonal systems,” which is particularly appropriate for classical variational expansions as applied to elliptic partial differential equations. For such systems, we obtain a number of a priori estimates of the asymptotic convergence rate which are easy to compute, and which are likely to be realistic in practice. In the simplest cases these estimates reduce the problem of variational convergence to the simpler problem of Fourier series convergence, which is considered in a companion paper. We also produce estimates for the convergence rate of the individual expansion coefficients $a_i^{(n)}$, thus categorising the convergence completely.
  • L. V. Kantorovič and V. I. Krylov, Približennye metody vysšego analiza, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1950 (Russian). 3d ed.]. MR 0042210
  • S. G. Mikhlin, Variational methods in mathematical physics, A Pergamon Press Book, The Macmillan Company, New York, 1964. Translated by T. Boddington; editorial introduction by L. I. G. Chambers. MR 0172493
  • C. Schwartz, Estimating Convergence Rates of Variational Calculations, Methods in Computational Physics, vol. 2, Academic Press, New York, 1963.
  • J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65N30
  • Retrieve articles in all journals with MSC: 65N30
Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 699-716
  • MSC: Primary 65N30
  • DOI:
  • MathSciNet review: 0311131