Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Equation Solving Generalized Inverses Read chapter Read first chapter

2018 | OriginalPaper | Chapter

7. Parallel Algorithms for Computing the Generalized Inverses

Authors : Guorong Wang, Yimin Wei, Sanzheng Qiao

Published in: Generalized Inverses: Theory and Computations

Publisher: Springer Singapore

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The UNIVersal Automatic Computer (UNIVAC I) and the machines built in 1940s and mid 1950s are often referred to as the first generation of computers.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Structured Matrices and Their Generalized Inverses
next chapter Perturbation Analysis of the Moore-Penrose Inverse and the Weighted Moore-Penrose Inverse
Literature
1.
2.
L. Kang et al., Asynchronous Parallel Algorithms for Solving the Problem of Mathematical Physics (Science Press, Beijing, 1985). in Chinese
3.
J.M. Ortega, R.G. Voigt, Solution of partial differential equations on vector and parallel computer. SIAM Review 27, 149–240 (1985)MathSciNetCrossRef
4.
J.M. Ortega, Introduction to Parallel and Vector Solution of Linear Systems (Plenum Press, New York, 1988)CrossRef
5.
O.Y. Devel, E.V. Krishnamurthy, An iterative pipelined arrary architecture for the generalized matrix inversion. Inform. Process. Lett. 26, 263–267 (1988)MathSciNetCrossRef
6.
G. Wang, L. Senquan, Fast parallel algorithm for computing the generalized inverses \(A^{\dagger }\) and \(A_{MN}^{\dagger }\). J. Comput. Math. 6, 348–354 (1988)MathSciNetMATH
7.
G. Wang, The Moore-Penrose inverse of bidiagonal matrices and its parallel algorithm. Numer. Math. J. Chinese Univ., 12, 14–23 (1990) (in Chinese)
8.
G. Wang, An improved parallel algorithm for computing the generalized inverse \(A^\dagger \). Inform. Process. Lett. 41, 243–251 (1992)MathSciNetCrossRef
9.
G. Wang, PCR algorithm for parallel computing minimum-norm least-squares solution of inconsistent linear equations. Numer. Math. J. Chinese Univ. English Series 2, 1–10 (1993)
10.
J. Chen, Parallel Numerical Methods (Qinghua Univ. Press, Beijing, 1983). in Chinese
11.
M.R. Zargham, Computer Architecture (Prentice-Hall Inc, Single and Paralled Systems, 1996)MATH
12.
J.J. Dongarra, I.S. Duff, D.C. Sorensen, van der Vorst, A. Henk, Solving Linear Systems on Vector and Shared Memory Computers. (Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1991)
13.
B. Zhang et al., Principles and Methods of Numerical Parallel Computation (National Defence Science and Technology Press, Beijing, 1999). in Chinese
14.
A.K. Chandra, Maximal parallelism in matrix multiplication. Technical Report RC-6139 (I.B.M. Watson Research Center, Yorktown Heights, N.Y., 1976)
15.
E.P. Preparata, D.V. Sarwate, An improved parallel processor bound in fast matrix inversion. Inform. Process. Lett. 7, 148–150 (1978)MathSciNetCrossRef
16.
A.H. Sameh, R.P. Brent, Solving triangular systems on a parallel computer. SIAM J. Numer. Anal. 14, 1101–1113 (1977)MathSciNetCrossRef
17.
18.
G. Wang, L. Senquan, Fast parallel algorithm for computing generalized inverses \(A^{\dagger }\) and \(A_{MN}^{\dagger }\). J. Shanghai Normal Univ. 16, 17–22 (1987). in Chinese
19.
L. Zhang et al., Design and Analysis of Parallel Algorithms (Hunan Science and Technology Press, Hunan, 1984). in Chinese
20.
B. Noble, J. Demmel, Applied Linear Algebra, 3rd edn. (Prentice-Hall, New Jersey, 1988)
21.
G. Wang, Y. Wei, PCR algorithm for the parallel computation of the solution of a class of singular equations. J. Shanghai Normal Univ. 23, 1–8 (1994)
22.
Y. Wei, G. Wang, PCR algorithm for parallel computing minimum-norm \((T)\) least-squares \((S)\) solution of inconsistent linear equations. Appl. Math. Comput. 133, 547–557 (2002)MathSciNetMATH
23.
M.K. Sridhar, A new algorithm for parallel solution of linear equations. Inform. Process. Lett. 24, 407–412 (1987)MathSciNetCrossRef
24.
G. Wang, Y. Wei, Parallel (\(M\)-\(N\))SVD algorithm on the SIMD computers. Wuhan Univ. J. Natural Sci., vol. 1, pp. 541–546. International Parallel Computing Conference (1996)
25.
L. Chen, E.V. Krishnamurthy, I. Madeod, Generalized matrix inversion and rank computation by successive matrix powering. Parallel Comput. 20, 297–311 (1994)MathSciNetCrossRef
26.
Y. Wei, Successive matrix squaring for computing the Drazin inverse. Appl. Math. Comput. 108, 67–75 (2000)MathSciNetMATH
27.
Y. Wei, W. Hebing, J. Wei, Successive matrix squaring algorithm for parallel computing the weighted generalized inverse \(A_{MN}^{\dagger }\). Appl. Math. Comput. 116, 289–296 (2000)MathSciNetMATH
28.
J. Wang, A recurrent neural networks for real-time matrix inversion. Appl. Math. Comput. 55, 23–34 (1993)CrossRef
29.
J. Wang, Recurrent neural networks for computing pseudoinverse of rank-deficient matrices. SIAM J. Sci. Comput. 18, 1479–1493 (1997)MathSciNetCrossRef
30.
Y. Wei, Recurrent neural networks for computing weighted Moore-Penrose inverse. Appl. Math. Comput. 116, 279–287 (2000)MathSciNetCrossRef
31.
G. Wang, Y. Wei, An improved parallel algorithm for computing the weighted Moore-Penrose inverse \(A_{MN}^{\dagger }\). J. Shanghai Normal Univ. 29, 12–20 (2000)
Metadata
Title
Parallel Algorithms for Computing the Generalized Inverses
Authors
Guorong Wang
Yimin Wei
Sanzheng Qiao
Copyright Year
2018
Publisher
Springer Singapore
Book
Generalized Inverses: Theory and Computations

Print ISBN: 978-981-13-0145-2

Electronic ISBN: 978-981-13-0146-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-981-13-0146-9_7

Premium Partner

    Image Credits