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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Finite-dimensional approximation of constrained Tikhonov-regularized solutions of ill-posed linear operator equations
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by A. Neubauer PDF
Math. Comp. 48 (1987), 565-583 Request permission


In this paper we derive conditions under which the finite-dimensional constrained Tikhonov-regularized solutions ${x_{\alpha ,{C_n}}}$ of an ill-posed linear operator equation $Tx = y$ (i.e., ${x_{\alpha ,{C_n}}}$ is the minimizing element of the functional ${\left \| {Tx - y} \right \|^2} + \alpha {\left \| x \right \|^2}$, $\alpha > 0$ in the closed convex set ${C_n}$, which is a finite-dimensional approximation of a closed convex set C) converge to the best approximate solution of the equation in C. Moreover, we develop an estimate for the approximation error, which is optimal for certain sets C and ${C_n}$. We present numerical results that verify the theoretical results.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 48 (1987), 565-583
  • MSC: Primary 65J10; Secondary 65R20
  • DOI:
  • MathSciNet review: 878691