|Table of Contents|

[1] Sheng Xingping, Chen Jianlong,. An explicit representation and computation for the outer inverse [J]. Journal of Southeast University (English Edition), 2020, 36 (1): 118-122. [doi:10.3969/j.issn.1003-7985.2020.01.015]
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An explicit representation and computation for the outer inverse()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
36
Issue:
2020 1
Page:
118-122
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2020-03-20

Info

Title:
An explicit representation and computation for the outer inverse
Author(s):
Sheng Xingping1;  2;  Chen Jianlong1
1School of Mathematics, Southeast University, Nanjing 211189, China
2School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, China
Keywords:
outer inverse;  explicit representation;  elementary operation;  computational complexity
PACS:
O151.21
DOI:
10.3969/j.issn.1003-7985.2020.01.015
Abstract:
First, an explicit representation A(2)T, S=(GA+E)-1G of the outer invers A(2)T, S for a matrix A∈Cm×n with the prescribed range T and null space S is derived, which is simpler than A(2)T, S=(GA+E)-1G-V(UV)-2UG proposed by Ji in 2005. Next, a new algorithm for computing the outer inverse A(2)T, S based on the improved representation A(2)T, S=(GA+E)-1G through elementary operations on an appropriate partitioned matrix ［GA InIn 0］ is proposed and investigated. Then, the computational complexity of the introduced algorithm is also analyzed in detail. Finally, two numerical examples are shown to illustrate that this method is correct.

References:

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Memo

Memo:
Biographies: Sheng Xingping(1976—), male, professor, doctor; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation item: The National Natural Science Foundation of China(No.11771076).
Citation: Sheng Xingping, Chen Jianlong. An explicit representation and computation for the outer inverse[J].Journal of Southeast University(English Edition), 2020, 36(1):118-122.DOI:10.3969/j.issn.1003-7985.2020.01.015.
Last Update: 2020-03-20