메뉴 건너뛰기




Volumn 2, Issue 1, 2000, Pages 50-59

The decompositional approach to matrix computation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0347737736     PISSN: 15219615     EISSN: None     Source Type: Journal    
DOI: 10.1109/5992.814658     Document Type: Article
Times cited : (61)

References (58)
  • 4
    • 0003407903 scopus 로고
    • Matrix Eigensystem Routines - Eispack Guide Extension
    • Springer-Verlag, New York
    • B.S. Garbow et al., "Matrix Eigensystem Routines - Eispack Guide Extension," Lecture Notes in Computer Science, Springer-Verlag, New York, 1977.
    • (1977) Lecture Notes in Computer Science
    • Garbow, B.S.1
  • 7
    • 0023983122 scopus 로고
    • An Extended Set of Fortran Basic Linear Algebra Subprograms
    • J.J. Dongarra et al., "An Extended Set of Fortran Basic Linear Algebra Subprograms," ACM Trans. Mathematical Software, Vol. 14, 1988, pp. 1-17.
    • (1988) ACM Trans. Mathematical Software , vol.14 , pp. 1-17
    • Dongarra, J.J.1
  • 8
    • 0025402476 scopus 로고
    • A Set of Level 3 Basic Linear Algebra Subprograms
    • J.J. Dongarra et al., "A Set of Level 3 Basic Linear Algebra Subprograms," ACM Trans. Mathematical Software, Vol. 16, 1990, pp. 1-17.
    • (1990) ACM Trans. Mathematical Software , vol.16 , pp. 1-17
    • Dongarra, J.J.1
  • 9
    • 0018515759 scopus 로고
    • Basic Linear Algebra Subprograms for Fortran Usage
    • C.L. Lawson et al., "Basic Linear Algebra Subprograms for Fortran Usage," ACM Trans. Mathematical Software, Vol. 5, 1979, pp. 308-323.
    • (1979) ACM Trans. Mathematical Software , vol.5 , pp. 308-323
    • Lawson, C.L.1
  • 12
    • 0039888117 scopus 로고
    • A Matrix Presentation of Least Squares and Correlation Theory with Matrix Justification of Improved Methods of Solution
    • P.S. Dwyer, "A Matrix Presentation of Least Squares and Correlation Theory with Matrix Justification of Improved Methods of Solution," Annals Math. Statistics, Vol. 15, 1944, pp. 82-89.
    • (1944) Annals Math. Statistics , vol.15 , pp. 82-89
    • Dwyer, P.S.1
  • 14
    • 0001252659 scopus 로고
    • Numerical Inverting of Matrices of High Order
    • J. von Neumann and H.H. Coldstine, "Numerical Inverting of Matrices of High Order," Bull. Am. Math. Soc., Vol. 53, 1947, pp. 1021-1099.
    • (1947) Bull. Am. Math. Soc. , vol.53 , pp. 1021-1099
    • Von Neumann, J.1    Coldstine, H.H.2
  • 17
    • 84945709312 scopus 로고
    • Error Analysis of Direct Methods of Matrix Inversion
    • J.H. Wilkinson, "Error Analysis of Direct Methods of Matrix Inversion," J. ACM, Vol. 8, 1961, pp. 281-330.
    • (1961) J. ACM , vol.8 , pp. 281-330
    • Wilkinson, J.H.1
  • 23
    • 0003668665 scopus 로고
    • Prentice-Hall, Englewood Cliffs, N.J., reissued with revisions by SIAM, Philadelphia
    • B.N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, N.J., 1980; reissued with revisions by SIAM, Philadelphia, 1998.
    • (1980) The Symmetric Eigenvalue Problem
    • Parlett, B.N.1
  • 29
    • 0041925806 scopus 로고
    • Note sur une méthode de résolution des équations normales provenant de l'application de la méthode des moindres cárres a un systém d'équations linéares en nombre inférieur 'a celui des inconnues. - Application de la méthode à la resolution d'un systéme défini d'équations linéares
    • Procédé du Commandant Cholesky
    • C. Benoît, "Note sur une méthode de résolution des équations normales provenant de l'application de la méthode des moindres cárres a un systém d'équations linéares en nombre inférieur 'a celui des inconnues. - application de la méthode à la resolution d'un systéme défini d'équations linéares (Procédé du Commandant Cholesky) [Note on a Method for Solving the Normal Equations Arising from the Application of the Method of Least Squares to a System of Linear Equations whose Number Is Less than the Number of Unknowns-Application of the Method to the Solution of a Definite System of Linear Equations]," Bullétin Géodésique (Toulouse), Vol. 2, 1924, pp. 5-77.
    • (1924) Bullétin Géodésique (Toulouse) , vol.2 , pp. 5-77
    • Benoît, C.1
  • 32
    • 0347847310 scopus 로고
    • Über einen algebraischen Fundamentalsatz und seine Anwendungen
    • C.G.J. Jacobi, "Über einen algebraischen Fundamentalsatz und seine Anwendungen [On a Fundamental Theorem in Algebra and Its Applications]," Journal für die reine und angewandte Mathematik, Vol. 53, 1857, pp. 275-280.
    • (1857) Journal für die Reine und Angewandte Mathematik , vol.53 , pp. 275-280
    • Jacobi, C.G.J.1
  • 33
    • 34250957105 scopus 로고
    • Zur Theorie der linearen und nichtlinearen Integralgleichungen. I Teil, Entwicklung willkürlichen Funktionen nach System vorgeschriebener
    • E. Schmidt, "Zur Theorie der linearen und nichtlinearen Integralgleichungen. I Teil, Entwicklung willkürlichen Funktionen nach System vorgeschriebener [On the Theory of Linear and Nonlinear Integral Equations. Part I, Expansion of Arbitrary Functions by a Prescribed System]," Mathematische Annalen, Vol. 63, 1907, pp. 433-476.
    • (1907) Mathematische Annalen , vol.63 , pp. 433-476
    • Schmidt, E.1
  • 35
    • 0000652188 scopus 로고
    • Unitary Triangularization of a Nonsymmetric Matrix
    • A.S. Householder, "Unitary Triangularization of a Nonsymmetric Matrix," J. ACM, Vol. 5, 1958, pp. 339-342.
    • (1958) J. ACM , vol.5 , pp. 339-342
    • Householder, A.S.1
  • 36
    • 85037509806 scopus 로고
    • Comparison of Least Squares Algorithms
    • Neutron Physics Div., Oak Ridge Nat'l Laboratory, Oak Ridge, Tenn.
    • D. Bogert and W.R. Burris, Comparison of Least Squares Algorithms, Tech. Report ORNL-3499, V.1, S5.5, Neutron Physics Div., Oak Ridge Nat'l Laboratory, Oak Ridge, Tenn., 1963.
    • (1963) Tech. Report ORNL-3499 , vol.1 , pp. 55
    • Bogert, D.1    Burris, W.R.2
  • 37
    • 0000924593 scopus 로고
    • Numerical Methods for Solving Least Squares Problems
    • G.H. Golub, "Numerical Methods for Solving Least Squares Problems," Numerische Mathematik, Vol. 7, 1965, pp. 206-216.
    • (1965) Numerische Mathematik , vol.7 , pp. 206-216
    • Golub, G.H.1
  • 38
    • 0000659575 scopus 로고
    • A Divide and Conquer Method for the Symmetric Eigenproblem
    • J.J.M. Cuppen, "A Divide and Conquer Method for the Symmetric Eigenproblem," Numerische Mathematik, Vol. 36, 1981, pp. 177-195.
    • (1981) Numerische Mathematik , vol.36 , pp. 177-195
    • Cuppen, J.J.M.1
  • 39
    • 21844525426 scopus 로고
    • Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem
    • M. Gu and S.C. Eisenstat, "Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem," SIAM J. Matrix Analysis and Applications, Vol. 15, 1994, pp. 1266-1276.
    • (1994) SIAM J. Matrix Analysis and Applications , vol.15 , pp. 1266-1276
    • Gu, M.1    Eisenstat, S.C.2
  • 41
    • 79952008327 scopus 로고
    • Sur l'equation á l'aide de laquelle on détermine les inégalites séculaires des mouvements des planétes
    • A.L. Cauchy, "Sur l'equation á l'aide de laquelle on détermine les inégalites séculaires des mouvements des planétes [On the Equation by which the Inequalities for the Secular Movement of Planets Is Determined]," Oeuvres Completes (II, e Séie), Vol. 9, 1829.
    • (1829) Oeuvres Completes (II, e Séie) , vol.9
    • Cauchy, A.L.1
  • 42
    • 84868361941 scopus 로고
    • Über ein leichtes Verfahren die in der Theorie der Säculärstörungen vorkommenden Gleichungen numerisch aufzulösen
    • C.G.J. Jacobi, "Über ein leichtes Verfahren die in der Theorie der Säculärstörungen vorkommenden Gleichungen numerisch aufzulösen [On an Easy Method for the Numerical Solution of the Equations that Appear in the Theory of Secular Perturbations]," Journal für die reine und angewandte Mathematik, Vol. 30, 1846, pp. 51-594.
    • (1846) Journal für die Reine und Angewandte Mathematik , vol.30 , pp. 51-594
    • Jacobi, C.G.J.1
  • 43
    • 0012666124 scopus 로고
    • Householder's Method for the Solution of the Algebraic Eigenvalue Problem
    • J.H. Wilkinson, "Householder's Method for the Solution of the Algebraic Eigenvalue Problem," Computer J., Vol. 3, 1960, pp. 23-27.
    • (1960) Computer J. , vol.3 , pp. 23-27
    • Wilkinson, J.H.1
  • 44
    • 84976855597 scopus 로고
    • Algorithm 432: The Solution of the Matrix Equation AX - BX = C
    • R.H. Bartels and G.W. Stewart, "Algorithm 432: The Solution of the Matrix Equation AX - BX = C," Comm. ACM, Vol. 8, 1972, pp. 820-826.
    • (1972) Comm. ACM , vol.8 , pp. 820-826
    • Bartels, R.H.1    Stewart, G.W.2
  • 45
    • 0018721357 scopus 로고
    • Hessenberg-Schur Method for the Problem AX + XB = C
    • G.H. Golub, S. Nash, and C. Van Loan, "Hessenberg-Schur Method for the Problem AX + XB = C," IEEE Trans. Automatic Control, Vol. AC-24, 1979, pp. 909-913.
    • (1979) IEEE Trans. Automatic Control , vol.AC-24 , pp. 909-913
    • Golub, G.H.1    Nash, S.2    Van Loan, C.3
  • 46
    • 0000394782 scopus 로고
    • The QR Transformation, Parts I and II
    • J.G.F. Francis, "The QR Transformation, Parts I and II," Computer J., Vol. 4, 1961, pp. 265-271, 1962, pp. 332-345.
    • (1961) Computer J. , vol.4 , pp. 265-271
    • Francis, J.G.F.1
  • 47
    • 0347217291 scopus 로고
    • J.G.F. Francis, "The QR Transformation, Parts I and II," Computer J., Vol. 4, 1961, pp. 265-271, 1962, pp. 332-345.
    • (1962) Computer J. , pp. 332-345
  • 48
    • 0001100568 scopus 로고
    • Über die charakteristischen Würzeln einer linearen Substitution mit einer Anwendung auf die Theorie der Integral gleichungen
    • J. Schur, "Über die charakteristischen Würzeln einer linearen Substitution mit einer Anwendung auf die Theorie der Integral gleichungen [On the Characteristic Roots of a Linear Transformation with an Application to the Theory of Integral Equations]," Mathematische Annalen, Vol. 66, 1909, pp. 448-510.
    • (1909) Mathematische Annalen , vol.66 , pp. 448-510
    • Schur, J.1
  • 51
    • 0347217290 scopus 로고
    • An English translation Dept. of Computer Science, Univ. of Minnesota, Minneapolis
    • An English translation by D. Boley is available in Tech. Report 90-37, Dept. of Computer Science, Univ. of Minnesota, Minneapolis, 1990.
    • (1990) Tech. Report 90-37
    • Boley, D.1
  • 53
    • 0000288016 scopus 로고
    • Calculating the Singular Values and Pseudo-Inverse of a Matrix
    • G.H. Golub and W. Kahan, "Calculating the Singular Values and Pseudo-Inverse of a Matrix," SIAM J. Numerical Analysis, Vol. 2, 1965, pp. 205-224.
    • (1965) SIAM J. Numerical Analysis , vol.2 , pp. 205-224
    • Golub, G.H.1    Kahan, W.2
  • 54
    • 0001211882 scopus 로고
    • Solution of Linear Systems by Diagonalization of Coefficients Matrix
    • E.G. Kogbetliantz, "Solution of Linear Systems by Diagonalization of Coefficients Matrix," Quarterly of Applied Math., Vol. 13, 1955, pp. 123-132.
    • (1955) Quarterly of Applied Math. , vol.13 , pp. 123-132
    • Kogbetliantz, E.G.1
  • 55
    • 0002170151 scopus 로고
    • Rank Revealing QR Factorizations
    • T.F. Chan, "Rank Revealing QR Factorizations," Linear Algebra and Its Applications, Vol. 88/89, 1987, pp. 67-82.
    • (1987) Linear Algebra and Its Applications , vol.88-89 , pp. 67-82
    • Chan, T.F.1
  • 56
    • 0026882267 scopus 로고
    • An Updating Algorithm for Subspace Tracking
    • G.W. Stewart, "An Updating Algorithm for Subspace Tracking," IEEE Trans. Signal Processing, Vol. 40, 1992, pp. 1535-1541.
    • (1992) IEEE Trans. Signal Processing , vol.40 , pp. 1535-1541
    • Stewart, G.W.1
  • 57
    • 0000166648 scopus 로고
    • Computing the Generalized Singular Value Decomposition
    • Z. Bai and J.W. Demmel, "Computing the Generalized Singular Value Decomposition," SIAM J. Scientific and Statistical Computing, Vol. 14, 1993, pp. 1464-1468.
    • (1993) SIAM J. Scientific and Statistical Computing , vol.14 , pp. 1464-1468
    • Bai, Z.1    Demmel, J.W.2
  • 58
    • 0000356673 scopus 로고
    • An Algorithm for Generalized Matrix Eigenvalue Problems
    • C.B. Moler and G.W. Stewart, "An Algorithm for Generalized Matrix Eigenvalue Problems," SIAM J. Numerical Analysis, Vol. 10, 1973, pp. 241-256.
    • (1973) SIAM J. Numerical Analysis , vol.10 , pp. 241-256
    • Moler, C.B.1    Stewart, G.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.