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Volumn 205, Issue 1, 2007, Pages 533-544

Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices

Author keywords

Accurate dot product; Ill conditioned matrix; Matrix inversion; Precondition

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; INFORMATION THEORY; NUMBER THEORY; PROBLEM SOLVING;

EID: 34247358712     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.05.022     Document Type: Article
Times cited : (20)

References (12)
  • 1
    • 34247348105 scopus 로고    scopus 로고
    • ANSI/IEEE, IEEE Standard for Binary Floating Point Arithmetic, Std 754-1985 ed., IEEE, New York, 1985.
  • 2
    • 0001345156 scopus 로고
    • Condition numbers and the distance to the nearest ill-posed problem
    • Demmel J.B. Condition numbers and the distance to the nearest ill-posed problem. Numer. Math. 51 (1987) 251-289
    • (1987) Numer. Math. , vol.51 , pp. 251-289
    • Demmel, J.B.1
  • 3
    • 0000802374 scopus 로고
    • The approximation of one matrix by another of lower rank
    • Eckhart C., and Young G. The approximation of one matrix by another of lower rank. Psychometrika 1 (1936) 211-218
    • (1936) Psychometrika , vol.1 , pp. 211-218
    • Eckhart, C.1    Young, G.2
  • 5
    • 0022676128 scopus 로고
    • The arithmetic of the digital computer: a new approach
    • Kulisch U.W., and Miranker W.L. The arithmetic of the digital computer: a new approach. SIAM Rev. 28 (1986) 1-40
    • (1986) SIAM Rev. , vol.28 , pp. 1-40
    • Kulisch, U.W.1    Miranker, W.L.2
  • 8
    • 34247331283 scopus 로고    scopus 로고
    • Numerical verification method for arbitrarily ill-conditioned linear systems
    • (in Japanese)
    • Ohta T., Ogita T., Rump S.M., and Oishi S. Numerical verification method for arbitrarily ill-conditioned linear systems. Trans. JSIAM 15 3 (2005) 269-287 (in Japanese)
    • (2005) Trans. JSIAM , vol.15 , Issue.3 , pp. 269-287
    • Ohta, T.1    Ogita, T.2    Rump, S.M.3    Oishi, S.4
  • 9
    • 34247394098 scopus 로고    scopus 로고
    • S.M. Rump, Approximate inverses of almost singular matrices still contain useful information, Technical Report 90.1, Faculty for Information and Communication Sciences, Hamburg University of Technology, 1990.
  • 10
    • 33746071070 scopus 로고
    • A class of arbitrarily ill-conditioned floating-point matrices
    • Rump S.M. A class of arbitrarily ill-conditioned floating-point matrices. SIAM J. Matrix Anal. Appl. 12 4 (1991) 645-653
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , Issue.4 , pp. 645-653
    • Rump, S.M.1
  • 11
    • 34247400607 scopus 로고    scopus 로고
    • S.M. Rump, T. Ogita, S. Oishi, Accurate floating-point summation, 41 pages, 2006, submitted for publication, preprint is available from 〈http://www.ti3.tu-harburg.de/publications/rump〉. Technical Report 05.12, Faculty for Information and Communication Sciences, Hamburg University of Technology, 2005.
  • 12
    • 34247333684 scopus 로고    scopus 로고
    • K. Tanabe, private communication.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.