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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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Error bounds on approximate solutions to systems of linear algebraic equations
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by A. de la Garza PDF
Math. Comp. 7 (1953), 81-84 Request permission
References
    The referee makes the following comments: “If all $|{d_{ij}}| > 0$, the optimum choice of $\gamma$ is unique and is the eigenvector ${u_1}$ of $\alpha (D)$ whose components are all positive, and $k$ is then the dominant eigenvalue ${\lambda _1}$ of $\alpha (D)$. This follows from a lemma that, since all ${g_i} > 0,{\lambda _1}$ lies strictly between the minimum and maximum of the ratios ${e’_i}\alpha (D)\gamma /{e’_i}\gamma$, unless the ratios are all equal (and hence equal to ${\lambda _1}$). The lemma is a slight extension of Theorem I of Hazel Perfect, ’On matrices with positive elements,’ Quart. Jn. of Math., s. 2, v. 2, 1951, p. 286-290. “The vector $\alpha ^{p}(D)e$, which is asymptotically a multiple of ${u_1}$ as $p \to \infty$, may be a useful approximation to $\gamma$ for sufficiently large $p$."
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Additional Information
  • © Copyright 1953 American Mathematical Society
  • Journal: Math. Comp. 7 (1953), 81-84
  • MSC: Primary 65.0X
  • DOI: https://doi.org/10.1090/S0025-5718-1953-0054340-8
  • MathSciNet review: 0054340