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Customizable triangular factorizations of matrices. (English) Zbl 1050.15012
The author obtains a number of matrix factorizations, where some of the factors are customized. Here ‘customized’ means having special entries which are particularly well suited for some applications, or allowing fast numerical calculations.
A typical result in the paper is the following:
Given the customized diagonal entries of an upper triangular matrix \(U\) as \(d_1,d_2,\ldots,d_N\), an \(N\times N\) matrix \(A\) has a PLUS factorization \(A= \text{PLUS}\) if and only if \(\det A=\pm d_1d_2\cdots d_N\neq0\), where \(P\) is a permutation or an upper pseudo-permutation matrix, \(L\) is a unit lower triangular matrix, \(S\) is a unit single-row matrix with \(N-1\) elements in the customized positions of \(S(N,k)\) for \(k=1,2,3,\ldots,N-1\), or \(S=I+e_Ns_N^T\).

MSC:
15A23 Factorization of matrices
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References:
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