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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 measures of ill-conditioning for nonlinear equations
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by Werner C. Rheinboldt PDF
Math. Comp. 30 (1976), 104-111 Request permission


Let ${x^\ast }$ be a solution of the nonlinear equation $Fx = b$ on a normed linear space and ${y^\ast }$ that of a perturbed equation $Gx = c$. Estimates for the relativized error between ${x^\ast }$ and ${y^\ast }$ are derived which extend a known estimate for the corresponding matrix case. The condition number of F depends now also on the domain, and special considerations are needed to determine the existence of the solution of the perturbed equation. For differentiable F, when the domain shrinks to a point, the condition number of F is shown to reduce to that of the derivative at that point.
  • George J. Fix and Kate Larsen, On the convergence of SOR iterations for finite element approximations to elliptic boundary value problems, SIAM J. Numer. Anal. 8 (1971), 536–547. MR 293859, DOI 10.1137/0708051
  • J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York-London, 1970. MR 0273810
  • R. S. Varga, Functional analysis and approximation theory in numerical analysis, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 3, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1971. MR 0310504
  • J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 104-111
  • MSC: Primary 65J05
  • DOI:
  • MathSciNet review: 0400702