Volume 6, Issue 4
Fast Parallel Algorithms for Computing Generalized Inverses A^+ and A_{MN}^+

Guo-rong Wang & Sen-quan Lu

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J. Comp. Math., 6 (1988), pp. 348-354

Published online: 1988-06

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  • Abstract

The parallel arithmetic complexities for computing generalized inverse $A^+$, computing the minimum-norm least-squares solution of Ax=b, computing order m+n-r determinants and finding the characteristic polynomials of order m+n-r matrices are shown to have the same grawth rate. Algorithms are given that compute $A^+$ and $A_{MN}^+$ in $O(\log r\dot \log n+\log m)$ and $O(\log^2n+\log m)$ steps using a number of processors which is a ploynomial in m,n and r $(A\in B_r^{m\times n},r=rank A)$.

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@Article{JCM-6-348, author = {Guo-rong Wang and Sen-quan Lu}, title = {Fast Parallel Algorithms for Computing Generalized Inverses A^+ and A_{MN}^+}, journal = {Journal of Computational Mathematics}, year = {1988}, volume = {6}, number = {4}, pages = {348--354}, abstract = { The parallel arithmetic complexities for computing generalized inverse $A^+$, computing the minimum-norm least-squares solution of Ax=b, computing order m+n-r determinants and finding the characteristic polynomials of order m+n-r matrices are shown to have the same grawth rate. Algorithms are given that compute $A^+$ and $A_{MN}^+$ in $O(\log r\dot \log n+\log m)$ and $O(\log^2n+\log m)$ steps using a number of processors which is a ploynomial in m,n and r $(A\in B_r^{m\times n},r=rank A)$. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9523.html} }
TY - JOUR T1 - Fast Parallel Algorithms for Computing Generalized Inverses A^+ and A_{MN}^+ AU - Guo-rong Wang & Sen-quan Lu JO - Journal of Computational Mathematics VL - 4 SP - 348 EP - 354 PY - 1988 DA - 1988/06 SN - 6 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/jcm/9523.html KW - AB - The parallel arithmetic complexities for computing generalized inverse $A^+$, computing the minimum-norm least-squares solution of Ax=b, computing order m+n-r determinants and finding the characteristic polynomials of order m+n-r matrices are shown to have the same grawth rate. Algorithms are given that compute $A^+$ and $A_{MN}^+$ in $O(\log r\dot \log n+\log m)$ and $O(\log^2n+\log m)$ steps using a number of processors which is a ploynomial in m,n and r $(A\in B_r^{m\times n},r=rank A)$.
Guo-rong Wang & Sen-quan Lu. (1970). Fast Parallel Algorithms for Computing Generalized Inverses A^+ and A_{MN}^+. Journal of Computational Mathematics. 6 (4). 348-354. doi:
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