منابع مشابه
The inverse of banded matrices
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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Block-banded matrices generalize banded matrices. We study the properties of positive definite full matrices whose inverses are -block-banded. We show that, for such matrices, the blocks in the -block band of completely determine ; namely, all blocks of outside its -block band are computed from the blocks in the -block band of . We derive fast inversion algorithms for and its inverse that, when...
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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...
متن کاملOn the nonnegative inverse eigenvalue problem of traditional matrices
In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2013
ISSN: 0377-0427
DOI: 10.1016/j.cam.2012.07.018