Block matrices with L-block-banded inverse: inversion algorithms
نویسندگان
چکیده
منابع مشابه
Block Matrices With -Block-banded Inverse: Inversion Algorithms
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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We investigate the properties of block matrices with block banded inverses to derive efficient matrix inversion algorithms for such matrices. In particular, we derive the following: (1) a recursive algorithm to invert a full matrix whose inverse is structured as a block tridiagonal matrix; (2) a recursive algorithm to compute the inverse of a structured block tridiagonal matrix. These algorithm...
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We provide a new representation for the inverse of block tridiagonal and banded matrices. The new representation is shown to be numerically stable over a variety of block tridiagonal matrices, in addition of being more computationally efficient than the previously proposed techniques. We provide two algorithms for commonly encountered problems that illustrate the usefulness of the results.
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The inversion problem for square matrices having the structure of a block Hankel-like matrix is studied. Examples of such matrices in&de Hankel striped, Hankel layered, and vector Hankel matrices. It is shown that the components that both determine nonsingularity and construct the inverse of such matrices are closely related to certain matrix polynomials. These matrix polynomials are multidimen...
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ژورنال
عنوان ژورنال: IEEE Transactions on Signal Processing
سال: 2005
ISSN: 1053-587X
DOI: 10.1109/tsp.2004.840709