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.


Convergence rates for regularized solutions
HTML articles powered by AMS MathViewer

by Mark A. Lukas PDF
Math. Comp. 51 (1988), 107-131 Request permission


Given a first-kind integral equation \[ \mathcal {K}u(x) = \int _0^1 {K(x,t)u(t) dt = f(x)} \] with discrete noisy data ${d_i} = f({x_i}) + {\varepsilon _i}$, $i = 1,2, \ldots ,n$, let ${u_{n\alpha }}$ be the minimizer in a Hilbert space W of the regularization functional $(1/n)\sum {(\mathcal {K}} u({x_i}) - {d_i}{)^2} + \alpha \left \| u \right \|_W^2$. It is shown that in any one of a wide class of norms, which includes ${\left \| \cdot \right \|_W}$, if $\alpha \to 0$ in a certain way as $n \to \infty$, then ${u_{n\alpha }}$ converges to the true solution ${u_0}$. Convergence rates are obtained and are used to estimate the optimal regularization parameter $\alpha$.
Similar Articles
Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 107-131
  • MSC: Primary 65R20; Secondary 41A25, 45L05
  • DOI:
  • MathSciNet review: 942146