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Mathematics of Computation

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Some properties of a class of band matrices

Authors: W. D. Hoskins and P. J. Ponzo
Journal: Math. Comp. 26 (1972), 393-400
MSC: Primary 65F30
MathSciNet review: 0303703
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Abstract: Let $ A(2r + 1,n)$ denote the $ n \times n$ band matrix, of bandwidth $ 2r + 1$, with the binomial coefficients in the expansion of $ {(x - 1)^{2r}}$ as the elements in each row and column. Using the fact that the rows of $ A(2r + 1,n)$ provide the coefficients for the $ 2r$th central difference, a number of properties of $ A(2r + 1,n)$ are obtained for all positive integers $ r$ and $ n$. These include obtaining explicit formulas for $ \det A(2r + 1,n),{A^{ - 1}}(2r + 1,n),\vert\vert{A^{ - 1}}(2r + 1,n)\vert{\vert _\infty }$ and an upper triangular matrix $ U$ such that $ A(2r + 1,n)U$ is lower triangular.

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

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Keywords: Determinants, band matrices, inverse matrices, norms on inverses
Article copyright: © Copyright 1972 American Mathematical Society

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