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Volumn 16, Issue 2, 1996, Pages 141-153

Pivoting strategies leading to small bounds of the errors for certain linear systems

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR SYSTEMS; NUMBER THEORY;

EID: 0040799576     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/16.2.141     Document Type: Article
Times cited : (8)

References (26)
  • 1
    • 0001366189 scopus 로고
    • Totally positive matrices
    • ANDO, T. 1987 Totally positive matrices. Linear Algebra Appl. 90, 165-219.
    • (1987) Linear Algebra Appl. , vol.90 , pp. 165-219
    • Ando, T.1
  • 2
    • 0000015959 scopus 로고
    • Solving sparse linear systems with sparse backward error
    • ARIOLI, M., DEMMEL, J., & DUFF, I. 1989 Solving sparse linear systems with sparse backward error. SIAM J. Matrix Anal. Appl. 10, 165-190.
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 165-190
    • Arioli, M.1    Demmel, J.2    Duff, I.3
  • 5
    • 0000396870 scopus 로고
    • Shape preserving representations and optimality of the Bernstein basis
    • CARNICER, J. M., & PEÑA, J. M. 1993 Shape preserving representations and optimality of the Bernstein basis. Adv. Comput. Math. 1, 173-196.
    • (1993) Adv. Comput. Math. , vol.1 , pp. 173-196
    • Carnicer, J.M.1    Peña, J.M.2
  • 6
    • 21344493989 scopus 로고
    • Least supported bases and local linear independence
    • CARNICER, J. M., & PEÑA, J. M. 1994 Least supported bases and local linear independence. Numer. Math. 67, 289-301.
    • (1994) Numer. Math. , vol.67 , pp. 289-301
    • Carnicer, J.M.1    Peña, J.M.2
  • 7
    • 0002530383 scopus 로고
    • The LU-factorization of totally positive matrices
    • CRYER, C. W. 1973 The LU-factorization of totally positive matrices. Linear Algebra Appl. 7, 83-92.
    • (1973) Linear Algebra Appl. , vol.7 , pp. 83-92
    • Cryer, C.W.1
  • 8
    • 0012087402 scopus 로고
    • Backward error analysis for totally positive linear systems
    • DE BOOR, C., & PINKUS, A. 1977 Backward error analysis for totally positive linear systems. Numer. Math. 27, 485-490.
    • (1977) Numer. Math. , vol.27 , pp. 485-490
    • De Boor, C.1    Pinkus, A.2
  • 9
    • 0000803454 scopus 로고
    • On matrices with non-positive off-diagonal elements
    • FIEDLER, M., & PTAK, V. 1962 On matrices with non-positive off-diagonal elements. Czech. Math. J. 12, 382-400.
    • (1962) Czech. Math. J. , vol.12 , pp. 382-400
    • Fiedler, M.1    Ptak, V.2
  • 10
    • 38249011045 scopus 로고
    • Total positivity and Neville elimination
    • GASCA, M., & PEÑA, J. M. 1992 Total positivity and Neville elimination. Linear Algebra Appl. 165, 25-44.
    • (1992) Linear Algebra Appl. , vol.165 , pp. 25-44
    • Gasca, M.1    Peña, J.M.2
  • 11
    • 21344483623 scopus 로고
    • Total positivity, QR factorization and Neville elimination
    • GASCA, M., & PEÑA, J. M. 1993a Total positivity, QR factorization and Neville elimination. SIAM J. Matrix Anal. Appl. 14, 1132-1140.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 1132-1140
    • Gasca, M.1    Peña, J.M.2
  • 12
    • 38249001242 scopus 로고
    • Scaled pivoting for Gaussian and Neville elimination for totally positive systems
    • GASCA, M., & PEÑA, J. M. 1993b Scaled pivoting for Gaussian and Neville elimination for totally positive systems. Appl. Numer. Math. 13, 345-355.
    • (1993) Appl. Numer. Math. , vol.13 , pp. 345-355
    • Gasca, M.1    Peña, J.M.2
  • 14
    • 0001075864 scopus 로고
    • The accuracy of solutions to triangular systems
    • HIGHAM, N. J. 1989 The accuracy of solutions to triangular systems. SIAM J. Numer. Anal. 26, 1253-1265.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1253-1265
    • Higham, N.J.1
  • 15
    • 0001283328 scopus 로고
    • Bounding the error in Gaussian elimination for tridiagonal systems
    • HIGHAM, N. J. 1990a Bounding the error in Gaussian elimination for tridiagonal systems. SIAM J. Matrix Anal. Appl. 11, 521-530.
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , pp. 521-530
    • Higham, N.J.1
  • 16
    • 0040785214 scopus 로고
    • How accurate is Gaussian elimination?
    • (D. F. Griffiths and G. A. Watson, eds). Essex: Longman Scientific and Technical
    • HIGHAM, N. J. 1990b How accurate is Gaussian elimination? Numerical Analysis 1989 (D. F. Griffiths and G. A. Watson, eds). Essex: Longman Scientific and Technical.
    • (1990) Numerical Analysis 1989
    • Higham, N.J.1
  • 17
    • 0039599497 scopus 로고
    • Correlation inequalities of coupled oscillators
    • LEFF, H. S. 1980 Correlation inequalities of coupled oscillators. J. Math. Phys. 12, 569-578.
    • (1980) J. Math. Phys. , vol.12 , pp. 569-578
    • Leff, H.S.1
  • 18
    • 0040190738 scopus 로고
    • Ein kriterium für den nachweis der totalnichtnegativität von bandmatrizen
    • METELMANN, K. 1973 Ein Kriterium für den Nachweis der Totalnichtnegativität von Bandmatrizen. Linear Algebra Appl. 7, 163-171.
    • (1973) Linear Algebra Appl. , vol.7 , pp. 163-171
    • Metelmann, K.1
  • 19
    • 0021310293 scopus 로고
    • Backward error analysis for linear systems associated with inverses of H-matrices
    • NEUMANN, M., & PLEMMONS, R. J. 1984 Backward error analysis for linear systems associated with inverses of H-matrices. BIT 24, 102-112.
    • (1984) BIT , vol.24 , pp. 102-112
    • Neumann, M.1    Plemmons, R.J.2
  • 20
    • 0039599469 scopus 로고
    • A geometric analysis of Gaussian elimination, I
    • POOLE, G., & NEAL, L. 1991 A geometric analysis of Gaussian elimination, I. Linear Algebra Appl. 149, 249-272.
    • (1991) Linear Algebra Appl. , vol.149 , pp. 249-272
    • Poole, G.1    Neal, L.2
  • 21
    • 0018492360 scopus 로고
    • Scaling for numerical stability in Gaussian elimination
    • SKEEL, R. D. 1979 Scaling for numerical stability in Gaussian elimination. J. Asoc. Comput. Mach. 26, 494-526.
    • (1979) J. Asoc. Comput. Mach. , vol.26 , pp. 494-526
    • Skeel, R.D.1
  • 22
    • 0012063377 scopus 로고
    • Forward error analysis of Gaussian elimination. Part II: Stability theorems
    • STUMMEL, F. 1985 Forward error analysis of Gaussian elimination. Part II: stability theorems. Numer. Math. 46, 397-415.
    • (1985) Numer. Math. , vol.46 , pp. 397-415
    • Stummel, F.1
  • 23
    • 21344496299 scopus 로고
    • Errors and perturbations in Vandermonde systems
    • VARAH, J. M. 1993 Errors and perturbations in Vandermonde systems. IMA J. Numer. Anal. 13, 1-12.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 1-12
    • Varah, J.M.1
  • 26
    • 0040785199 scopus 로고
    • The inverse M-matrix problem
    • WILLOUGHBY, R. A. 1977 The inverse M-matrix problem. Linear Algebra Appl. 18, 75-94.
    • (1977) Linear Algebra Appl. , vol.18 , pp. 75-94
    • Willoughby, R.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.