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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
Full Text:
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