Computing \(A^ T A-B^ T B=L^ T DL\) using generalized hyperbolic transformations (Q1318226)
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scientific article; zbMATH DE number 540066
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Computing \(A^ T A-B^ T B=L^ T DL\) using generalized hyperbolic transformations |
scientific article; zbMATH DE number 540066 |
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Computing \(A^ T A-B^ T B=L^ T DL\) using generalized hyperbolic transformations (English)
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9 October 1994
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This paper describes generalized hyperbolic Householder and Givens transformations based on hyperbolic imaginary numbers for the computation of the \(L^ T DL\) factorization of the matrix \(Y = A^ T A - B^ T B\). The algorithms for extending the Householder and Givens transformations to hyperbolic complex numbers are given. \(L^ T DL\) decompositions using hyperbolic and generalized hyperbolic transformations are implemented and compared with the LINPACK subroutine SSIFA and SSISL in computing the inverse of a matrix. The relative errors of several computed inverses are calculated in the Frobenius norm.
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matrix inversion
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hyperbolic Householder transformation
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hyperbolic Givens transformation
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matrix factorization
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comparison of methods
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hyperbolic complex numbers
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