Some properties of a class of band matrices
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- by W. D. Hoskins and P. J. Ponzo PDF
- Math. Comp. 26 (1972), 393-400 Request permission
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 $\det A(2r + 1,n),{A^{ - 1}}(2r + 1,n),||{A^{ - 1}}(2r + 1,n)|{|_\infty }$ and an upper triangular matrix $U$ such that $A(2r + 1,n)U$ is lower triangular.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 393-400
- MSC: Primary 65F30
- DOI: https://doi.org/10.1090/S0025-5718-1972-0303703-3
- MathSciNet review: 0303703