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Mathematics of Computation

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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}$.

References [Enhancements On Off] (What's this?)

  • [1] H. W. Milnes, ``A note concerning the properties of a certain class of matrices,'' Math. Comp., v. 22, 1968, pp. 827-832. MR 0239743 (39:1100)

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Article copyright: © Copyright 1969 American Mathematical Society

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