zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Successive matrix squaring algorithm for parallel computing the weighted generalized inverse $A^+_{MN}$. (English) Zbl 1023.65031
Summary: We derive a successive matrix squaring algorithm to approximate the weighted generalized inverse, which can be expressed in the form of successive squaring of a composite matrix $T$. Given an $m$ by $n$ matrix $A$ with $m\approx n$, we show that the weighted generalized inverse of $A$ can be computed in parallel time ranging from $O(\log n)$ to $O(\log^2n)$ provided that there are enough processors to support matrix multiplication in time $O(\log n)$.

65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
65Y05Parallel computation (numerical methods)
Full Text: DOI
[1] A. Ben-Israel, T.N.E. Greville, Generalized Inverse: Theory and Applications, Wiley, New York, 1974
[2] A. Bjorck, Least squares methods in handbook of numerical analysis, in: P.G. Ciarlet, J.L. Lions (Eds.), Finite Difference Methods Solutions of Equations in Rn, vol. 1, North-Holland, Amsterdam, 1990
[3] Chen, L.; Krishnamurthy, E. V.; Madeod, I.: Generalized matrix inversion and rank computation by successive matrix powering. Parallel computing 20, 297-311 (1994) · Zbl 0796.65055
[4] Van Loan, C. F.: Generalizing the singular value decomposition. SIAM J. Numer. anal. 13, 76-83 (1976) · Zbl 0338.65022
[5] Wang, G.: A finite algorithm for computing the weighted Moore--Penrose inverse AMN+. Appl. math. Comput. 23, 277-289 (1987) · Zbl 0635.65039
[6] Wang, G.; Lu, S.: Fast parallel algorithm for computing the generalized inverse A+ and AMN+. J. comput. Math. 6, 348-354 (1988) · Zbl 0665.65037
[7] G. Wang, Y. Wei, PCR algorithm for parallel computing the minimum T-norm S-least squares solution of inconsistent linear equations, in: Proceedings of the Fourth National Parallel Computing Conference, Aviation Industry Press, Nanjing, China, 1993, pp. 87--92
[8] Wang, G.; Wei, Y.: The iterative methods for computing the generalized inverse AMN+ and ad,w. Numer. math. J. chinese universities 16, 366-372 (1994) · Zbl 0821.65022
[9] G. Wang, Y. Wei, Parallel (M--N) SVD algorithms on the SIMD computers, in: Proceedings of the International Parallel Computing Conference, Wuhan University, J. Natural Sci. 1 (1996) 541--546 · Zbl 0919.68068
[10] Sun, W.; Wei, Y.: Inverse order rule for weighted generalized inverse. SIAM J. Matrix anal. Appl. 19, 772-775 (1998) · Zbl 0911.15004
[11] Y. Wei, Perturbation and computation of generalized inverse A(2)T,S, Master thesis, Department of Mathematics, Shanghai Normal University, Shanghai, China, 1994
[12] Y. Wei, Solving singular linear systems and generalized inverses, PhD thesis, Institute of Mathematics, Fudan University, Shanghai, China, 1997
[13] Wei, Y.: Recurrent neural networks for computing weighted Moore--Penrose inverse. Appl. math. Comput. 116, 279-287 (2000) · Zbl 1023.65030
[14] Wei, Y.: Perturbation bound of singular linear system. Appl. math. Comput. 105, 211-220 (1999) · Zbl 1022.65042