메뉴 건너뛰기




Volumn 18, Issue 1, 2011, Pages 41-54

A backward stability analysis of diagonal pivoting methods for solving unsymmetric tridiagonal systems without interchanges

Author keywords

Normwise backward stability; Tridiagonal matrices; Unsymmetric indefinite factorization

Indexed keywords


EID: 78651428125     PISSN: 10705325     EISSN: 10991506     Source Type: Journal    
DOI: 10.1002/nla.674     Document Type: Article
Times cited : (4)

References (18)
  • 1
    • 84966231631 scopus 로고
    • A look-ahead Lánczos algorithm for unsymmetric matrices
    • Parlett BN, Taylor DR, Liu ZA. A look-ahead Lánczos algorithm for unsymmetric matrices. Mathematics of Computation 1985; 44(169):105-124.
    • (1985) Mathematics of Computation , vol.44 , Issue.169 , pp. 105-124
    • Parlett, B.N.1    Taylor, D.R.2    Liu, Z.A.3
  • 2
    • 0008838250 scopus 로고
    • A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems
    • Bank RE, Chan TF. A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems. Numerical Algorithms 1994; 7(1):1-16.
    • (1994) Numerical Algorithms , vol.7 , Issue.1 , pp. 1-16
    • Bank, R.E.1    Chan, T.F.2
  • 5
    • 84966228742 scopus 로고
    • Some stable methods for calculating inertia and solving symmetric linear systems
    • Bunch JR, Kaufman L. Some stable methods for calculating inertia and solving symmetric linear systems. Mathematics of Computation 1977; 31(137):163-179.
    • (1977) Mathematics of Computation , vol.31 , Issue.137 , pp. 163-179
    • Bunch, J.R.1    Kaufman, L.2
  • 6
    • 0015200767 scopus 로고
    • Direct methods for solving symmetric indefinite systems of linear equations
    • Bunch JR, Parlett BN. Direct methods for solving symmetric indefinite systems of linear equations. SIAM Journal on Numerical Analysis 1971; 8:639-655.
    • (1971) SIAM Journal on Numerical Analysis , vol.8 , pp. 639-655
    • Bunch, J.R.1    Parlett, B.N.2
  • 8
    • 0016072422 scopus 로고
    • Partial pivoting strategies for symmetric matrices
    • Bunch JR. Partial pivoting strategies for symmetric matrices. SIAM Journal on Numerical Analysis 1974; 11:521-528.
    • (1974) SIAM Journal on Numerical Analysis , vol.11 , pp. 521-528
    • Bunch, J.R.1
  • 9
    • 0040814438 scopus 로고    scopus 로고
    • T factorization of a symmetric tridiagonal matrix
    • celebrating the 60th birthday of Ludwig Elsner.
    • T factorization of a symmetric tridiagonal matrix. Linear Algebra and its Applications 1999; 287(1-3):181-189. Special issue celebrating the 60th birthday of Ludwig Elsner.
    • (1999) Linear Algebra and its Applications , vol.287 , Issue.1-3 SPEC. ISSUE , pp. 181-189
    • Higham, N.J.1
  • 11
    • 33845614423 scopus 로고    scopus 로고
    • A simplified pivoting strategy for symmetric tridiagonal matrices
    • Bunch JR, Marcia RF. A simplified pivoting strategy for symmetric tridiagonal matrices. Numerical Linear Algebra with Applications 2006; 13(10):865-867.
    • (2006) Numerical Linear Algebra with Applications , vol.13 , Issue.10 , pp. 865-867
    • Bunch, J.R.1    Marcia, R.F.2
  • 12
    • 39649090964 scopus 로고    scopus 로고
    • On solving sparse symmetric linear systems whose definiteness is unknown
    • Marcia RF. On solving sparse symmetric linear systems whose definiteness is unknown. Applied Numerical Mathematics 2008; 58(4):449-458.
    • (2008) Applied Numerical Mathematics , vol.58 , Issue.4 , pp. 449-458
    • Marcia, R.F.1
  • 14
    • 0000497979 scopus 로고
    • A completed theory of the unsymmetric Lanczos process and related algorithms, part I
    • Gutknecht M. A completed theory of the unsymmetric Lanczos process and related algorithms, part I. SIAM Journal on Matrix Analysis and Applications 1992; 13(2):594-639.
    • (1992) SIAM Journal on Matrix Analysis and Applications , vol.13 , Issue.2 , pp. 594-639
    • Gutknecht, M.1
  • 15
    • 0040876954 scopus 로고
    • Lanczos maximal algorithm for unsymmetric eigenvalue problems
    • Khelifi M. Lanczos maximal algorithm for unsymmetric eigenvalue problems. Applied Numerical Mathematics 1991; 7:179-193.
    • (1991) Applied Numerical Mathematics , vol.7 , pp. 179-193
    • Khelifi, M.1
  • 16
    • 0031538118 scopus 로고    scopus 로고
    • Stability of the diagonal pivoting method with partial pivoting
    • Higham NJ. Stability of the diagonal pivoting method with partial pivoting. SIAM Journal on Matrix Analysis and Applications 1997; 18(1):52-65.
    • (1997) SIAM Journal on Matrix Analysis and Applications , vol.18 , Issue.1 , pp. 52-65
    • Higham, N.J.1
  • 17
    • 0036457301 scopus 로고    scopus 로고
    • Accuracy and stability of numerical algorithms
    • (2nd edn). Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA.
    • Higham NJ. Accuracy and stability of numerical algorithms (2nd edn). Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA, 2002.
    • (2002)
    • Higham, N.J.1
  • 18
    • 33845220799 scopus 로고
    • Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
    • Oettli W, Prager W. Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides. Numerische Mathematik 1964; 6:405-409.
    • (1964) Numerische Mathematik , vol.6 , pp. 405-409
    • Oettli, W.1    Prager, W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.