Error bounds on approximate solutions to systems of linear algebraic equations

Author:
A. de la Garza

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

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**[1]**The referee makes the following comments: ``If all , the optimum choice of is unique and is the eigenvector of whose components are all positive, and is then the dominant eigenvalue of . This follows from a lemma that, since all lies strictly between the minimum and maximum of the ratios , unless the ratios are all equal (and hence equal to ). 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 , which is asymptotically a multiple of as , may be a useful approximation to for sufficiently large ."

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DOI:
https://doi.org/10.1090/S0025-5718-1953-0054340-8

Article copyright:
© Copyright 1953
American Mathematical Society