Groups of banded matrices with banded inverses
نویسندگان
چکیده
منابع مشابه
Groups of banded matrices with banded inverses
AproductADF1 : : : FN of invertible block-diagonalmatrices will be bandedwith a banded inverse. We establish this factorization with the numberN controlled by the bandwidthsw and not by the matrix size n:When A is an orthogonal matrix, or a permutation, or banded plus finite rank, the factors Fi have w D 1 and generate that corresponding group. In the case of infinite matrices, conjectures rema...
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It is unusual for both A and A(-1) to be banded--but this can be a valuable property in applications. Block-diagonal matrices F are the simplest examples; wavelet transforms are more subtle. We show that every example can be factored into A = F(1)...F(N) where N is controlled by the bandwidths of A and A(-1) (but not by their size, so this extends to infinite matrices and leads to new matrix gr...
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Abstract. If A is a banded matrix with a banded inverse, then A = BC = F1 . . . FN is a product of block-diagonal matrices. We review this factorization, in which the Fi are tridiagonal and N is independent of the matrix size. For a permutation with bandwidth w, each Fi exchanges disjoint pairs of neighbors and N < 2w. This paper begins the extension to infinite matrices. For doubly infinite pe...
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1. Background There are various methods for finding inverses of matrices (if these exist), and we recall the Gauss–Jordan method, the triangular decomposition such as LUD or Cholesky factorization, to mention only a few. A very popular approach is based on block partitioning. Let A = A11 A12 A21 A22 whose inverse (called Schur’s complement) is A−1 = A 11 + A −1 11 A12B A21A 11 −A −1 11 A1...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-10959-6