article

Free access

An Elimination Method for Computing the Generalized Inverse of an Arbitrary Complex Matrix

Authors:

A. Ben-Israel,

S. J. WersanAuthors Info & Claims

Journal of the ACM (JACM), Volume 10, Issue 4

Pages 532 - 537

https://doi.org/10.1145/321186.321197

Published: 01 October 1963 Publication History

PDF eReader

References

[1]

BEN-Isn.XL A., AND CHArtNES, A. Contributions to the theory of generalized inverses. J. SIAM (1963).

Google Scholar

[2]

BEN-ISAL, A., AND IJIaI, Y. A report on the machine calculation of the generMized inverse. Carnegie Inst. Tech., Pittsburgh, Penn., Mar. 1963.

Google Scholar

[3]

BJEAn, A. Application of calculus of matrices to method of least squares; with special reference to geodetic calculations. Trans. Roy. Inst. Tech. Stockholm 49 (1951), 1-86.

Google Scholar

[4]

----. tCectangular reciprocal matrices with special reference to geodetic cMculations. Bull. Geodesique (1951), 188--220.

Google Scholar

[5]

DEN BOEIzm, G. G., J., AND CHARNS, A. Contributions to the theory of a generalized inverse for matrices. Purdue University, Lafayette, Ill., 1957). Republished as 0NR Research Memo No. 39 Northwestern Univ., The Teeh. Inst., Evanston, II1. 1962.

Google Scholar

[6]

CLINZJ, i. E. On the computation of the generalized inverse A, of an arbitrary matrix A, and the use of certain associated eigenvectors in solving the allocation problem. Preliminary report, Purdue Univ., Statistical and Computing Lab., Lafayette, Ill., (1958).

Google Scholar

[7]

GREVILLE, T. N.E. The pseudo inverse of a rectangular or singular matrix and its applications to the solution of system of linear equations. SIAM Rev. I (1959) 38-43.

Google Scholar

[8]

----. Some applications of the pseudo inverse of a matrix. SIAM Rev. 2, 1 (1960) 15--22.

Digital Library

Google Scholar

[9]

HESTENS, M.R. Inversion of matrices by biorthogonalization and related results. J. SIAM G (1958) 84.

Google Scholar

[10]

--. Relative Hermitian matrices. Pacific J . Math. 11, 1 (1961) 225-245.

Google Scholar

[11]

--. A ternary algebra with applications to matrices and linear transformations. Arch. Rat. Mech. Anal. 11, 2 (1962), 138-194.

Google Scholar

[12]

MooRs, E.H. Bull. Amer. Math. Soc. 6 (1920), 394-395.

Google Scholar

[13]

----. (General Analysis, Pt I. Memoir Amer. Philos. Soc. I (1935).

Google Scholar

[14]

PENR0SE, R. A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51, 3 (1955) 406-413.

Google Scholar

[15]

--. On best approximate solution of linear matrix equations. Proc. Camb. Philos. Soc. 5Z, 1 (1956), 17-19.

Google Scholar

[16]

PYLE, L.D. A gradient projection method for solving programming problems using the generalized inverse A + and the eigenvectors e (1), .., e (n) of I - AA. Preliminary Report, Purdue Univ. Statistical and Computing Lab., Lafayette, Ind., 1958.

Google Scholar

Cited By

View all

ADACHI FTAKEDA KOBARA TYAMAMOTO TMATSUDA H(2010)Recent Advances in Single-Carrier Frequency-Domain Equalization and Distributed Antenna NetworkIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences10.1587/transfun.E93.A.2201E93-A:11(2201-2211)Online publication date: 2010
https://doi.org/10.1587/transfun.E93.A.2201
YAMAMOTO TTAKEDA KADACHI F(2010)Frequency-Domain Block Signal Detection for Single-Carrier TransmissionIEICE Transactions on Communications10.1587/transcom.E93.B.2104E93-B:8(2104-2112)Online publication date: 2010
https://doi.org/10.1587/transcom.E93.B.2104
Mohsen AStoer J(2001)A Variable Metric Method for Approximating Generalized Inverses of MatricesZAMM10.1002/1521-4001(200107)81:7<435::AID-ZAMM435>3.0.CO;2-581:7(435-446)Online publication date: Jul-2001
https://doi.org/10.1002/1521-4001(200107)81:7<435::AID-ZAMM435>3.0.CO;2-5
Show More Cited By

Index Terms

An Elimination Method for Computing the Generalized Inverse of an Arbitrary Complex Matrix
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices

Recommendations

A note on computing matrix-vector products with generalized centrosymmetric (centrohermitian) matrices

To reduce the costs of computing matrix-vector product Ax related to a centrosymmetric matrix A as compared to the case of an arbitrary matrix A, two algorithms were proposed recently, one was designed by Melman [A. Melman, Symmetric centrosymmetric ...
A new method for computing Moore-Penrose inverse through Gauss-Jordan elimination

Performing elementary row operations on [ A | I ] , we can calculate matrices whose columns form bases for N ( A ) and N ( A ) easily. These matrices are then used to construct a bordered matrix through which the Moore-Penrose inverse A of a general ...
The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices

A matrix <italic>P</italic> is called a symmetric orthogonal if <italic>P</italic> = <italic>P</italic>^{<italic>T</italic>} = <italic>P</italic>⁻¹. A matrix <italic>X</italic> is said to be a generalised bisymmetric with respect to <italic>P</italic> if <...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

Journal of the ACM Volume 10, Issue 4

Oct. 1963

169 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321186

Editor:
Richard W. Hamming

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1963

Published in JACM Volume 10, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

25
Total Citations
View Citations
638
Total Downloads

Downloads (Last 12 months)52
Downloads (Last 6 weeks)6

Reflects downloads up to 19 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

ADACHI FTAKEDA KOBARA TYAMAMOTO TMATSUDA H(2010)Recent Advances in Single-Carrier Frequency-Domain Equalization and Distributed Antenna NetworkIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences10.1587/transfun.E93.A.2201E93-A:11(2201-2211)Online publication date: 2010
https://doi.org/10.1587/transfun.E93.A.2201
YAMAMOTO TTAKEDA KADACHI F(2010)Frequency-Domain Block Signal Detection for Single-Carrier TransmissionIEICE Transactions on Communications10.1587/transcom.E93.B.2104E93-B:8(2104-2112)Online publication date: 2010
https://doi.org/10.1587/transcom.E93.B.2104
Mohsen AStoer J(2001)A Variable Metric Method for Approximating Generalized Inverses of MatricesZAMM10.1002/1521-4001(200107)81:7<435::AID-ZAMM435>3.0.CO;2-581:7(435-446)Online publication date: Jul-2001
https://doi.org/10.1002/1521-4001(200107)81:7<435::AID-ZAMM435>3.0.CO;2-5
Lakshmikantham VSen SSivasundaram S(1994)Concise row-pruning algorithm to invert a matrixApplied Mathematics and Computation10.1016/0096-3003(94)90143-061:1(17-24)Online publication date: 1-Mar-1994
https://dl.acm.org/doi/10.1016/0096-3003%2894%2990143-0
Faddeev DFaddeeva V(1981)Computational methods of linear algebraJournal of Soviet Mathematics10.1007/BF0108654415:5(531-650)Online publication date: 1981
https://doi.org/10.1007/BF01086544
Tanabe K(1977)Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrixJournal of Optimization Theory and Applications10.1007/BF0093671522:1(1-23)Online publication date: May-1977
https://doi.org/10.1007/BF00936715
Nashed MRall L(1976)Annotated Bibliography on Generalized Inverses and ApplicationsGeneralized Inverses and Applications10.1016/B978-0-12-514250-2.50018-4(771-1041)Online publication date: 1976
https://doi.org/10.1016/B978-0-12-514250-2.50018-4
Huang H(1975)A direct method for the general solution of a system of linear equationsJournal of Optimization Theory and Applications10.1007/BF0093385216:5-6(429-445)Online publication date: 1-Sep-1975
https://dl.acm.org/doi/10.1007/BF00933852
Chen R(1973)New Matrix Inversion Algorithms Based on Exchange MethodIEEE Transactions on Computers10.1109/T-C.1973.22361322:10(885-890)Online publication date: 1-Oct-1973
https://dl.acm.org/doi/10.1109/T-C.1973.223613
(1972)ReferencesRegression and the Moore-Penrose Pseudoinverse10.1016/S0076-5392(08)62927-6(173-176)Online publication date: 1972
https://doi.org/10.1016/S0076-5392(08)62927-6
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

References

Cited By

Index Terms

Recommendations

A note on computing matrix-vector products with generalized centrosymmetric (centrohermitian) matrices

A new method for computing Moore-Penrose inverse through Gauss-Jordan elimination

The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations