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...
متن کاملFast transforms: Banded matrices with banded inverses.
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...
متن کاملBanded Matrices with Banded Inverses and A = LPU
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...
متن کاملOn generalized inverses of banded matrices
Bounds for the ranks of upper-right submatrices of a generalized inverse of a strictly lower k-banded matrix are obtained. It is shown that such ranks can be exactly predicted under some conditions. The proof uses the Nullity Theorem and bordering technique for generalized inverse.
متن کاملBounds for Inverses of Triangular Toeplitz Matrices
This short note provides an improvement on a recent result of Vecchio on a norm bound for the inverse of a lower triangular Toeplitz matrix with nonnegative entries. A sharper asymptotic bound is obtained as well as a version for matrices of finite order. The results are shown to be nearly best possible under the given constraints. 1. Introduction. This paper provides an improvement on a recent...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1984
ISSN: 0024-3795
DOI: 10.1016/0024-3795(84)90182-4