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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

A generalization of a class of test matrices


Author: Robert J. Herbold
Journal: Math. Comp. 23 (1969), 823-826
MSC: Primary 65.35
MathSciNet review: 0258259
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Abstract: We consider matrices of the following form: $ {G_n}({a_1},{a_2}, \cdots ,{a_{n - 1}},{b_1},{b_2} \cdots {b_n}) = $ $ ({\beta _{i,j}}),1 \leqq i$, $ j \leqq n$, where $ {a_1}, \cdots ,{a_{n - 1}},{b_1}, \cdots ,{b_n}$ are constants and

$\displaystyle {\beta _i}_{,j} = {b_j},{\text{ }}j \geqq i;{\text{ }}{\beta _{ij}} = {a_j},{\text{ }}j < i.$

We deduce in analytic form the determinant, inverse matrix, characteristic equation, and eigenvectors of $ {G_n}$. Knowing these properties enables us to generate valuable test matrices by appropriately selecting the order and elements of $ {G_n}$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0258259-0
PII: S 0025-5718(1969)0258259-0
Article copyright: © Copyright 1969 American Mathematical Society