ジーン・ゴラブ

出典: フリー百科事典『ウィキペディア(Wikipedia)』

出典: フリー百科事典『ウィキペディア(Wikipedia)』

ジーン・ゴラブ (Gene Golub, 1932年2月29日 - 2007年11月16日) は数値解析数値線形代数を専門とするアメリカ合衆国の数学者である。

著書[編集]

  • Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms, Gene H. Golub, Published by Springer-Verlag (1991) ISBN 0387523006 ISBN 9780387523002
  • Matrix Computations, Gene H. Golub, Published by North Oxford Academic (1983) ISBN 0946536058 ISBN 9780946536054
  • Numerical Analysis (Proceedings of Symposia in Applied Mathematics, V. 22) Golub, Gene H., Oliger, Joseph, Published by American Mathematical Society (1978) ISBN 0821801228 ISBN 9780821801222
  • Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) Gene H. Golub, Charles F. Van Loan, Published by The Johns Hopkins University Press, ISBN 0801830117 ISBN 9780801830112
  • Scientific Computing: An Introduction with Parallel Computing, James M. Ortega; Gene H. Golub, Published by Elsevier Science & Technology Books, ISBN 0122892534 ISBN 9780122892530
  • Studies in Numerical Analysis. Studies in Mathematics, Volume 24, Golub, Gene H., editor, Published by Mathematical Association of America (1984) ISBN 0883851261 ISBN 9780883851265
  • Scientific Computing and Differential Equations: An Introduction to Numerical Methods, Gene H. Golub, James M. Ortega, Published by Academic Press (1992) ISBN 0122892550 ISBN 9780122892554
  • Recent Advances in Numerical Analysis, Carl de Boor and Gene H. Golub: Published by Academic Press Inc, 05.03.1979. (1979) ISBN 0122083601 ISBN 9780122083600

代表的な論文[編集]

単著[編集]

共著[編集]

1960年代[編集]

  • Golub, G. H., & Varga, R. S. (1961). Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. en:Numerische Mathematik, 3(1), 157-168.
  • Golub, G., & Kahan, W. (1965). Calculating the singular values and pseudo-inverse of a matrix. Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis, 2(2), 205-224.

1970年代[編集]

  • Buzbee, B. L., Golub, G. H., & Nielson, C. W. (1970). On direct methods for solving Poisson’s equations. en:SIAM Journal on Numerical Analysis, 7(4), 627-656.
  • Golub, G. H., & Pereyra, V. (1973). The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. en:SIAM Journal on Numerical Analysis, 10(2), 413-432.
  • Golub, G. H., & Styan, G. P. (1973). Numerical computations for univariate linear models. Journal of Statistical Computation and Simulation, 2(3), 253-274.
  • Concus, P., & Golub, G. H. (1973). Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. en:SIAM Journal on Numerical Analysis, 10(6), 1103-1120.
  • Björck, Ȧ., & Golub, G. H. (1973). Numerical methods for computing angles between linear subspaces. en:Mathematics of Computation, 27(123), 579-594.
  • De Boor, C., & Golub, G. H. (1978). The numerically stable reconstruction of a Jacobi matrix from spectral data. Linear Algebra and Its Applications, 21(3), 245-260.
  • Concus, P., Golub, G. H., & O'Leary, D. P. (1978). Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method. Computing, 19(4), 321-339.

1980年代[編集]

  • Golub, G. H., & Van Loan, C. F. (1980). An analysis of the total least squares problem. en:SIAM Journal on Numerical Analysis, 17(6), 883-893.
  • Chan, T. F., Golub, G. H., & LeVeque, R. J. (1983). Algorithms for computing the sample variance: Analysis and recommendations. The American Statistician, 37(3), 242-247.
  • Boley, D. L., & Golub, G. H. (1984). The Lanczos-Arnoldi algorithm and controllability. Systems and Control Letters, 4(6), 317-324.
  • Golub, G. H., & O’Leary, D. P. (1989). Some history of the conjugate gradient and Lanczos algorithms: 1948–1976. SIAM Review, 31(1), 50-102.
  • Gander, W., Golub, G. H., & von Matt, U. (1989). A constrained eigenvalue problem. Linear Algebra and its Applications, 114, 815-839.

1990年代[編集]

  • Comon, P., & Golub, G. H. (1990). Tracking a few extreme singular values and vectors in signal processing. Proceedings of the IEEE, 78(8), 1327-1343.
  • Gander, W., Golub, G. H., & Strebel, R. (1994). Least-squares fitting of circles and ellipses. en:BIT Numerical Mathematics, 34(4), 558-578.
  • Elman, H. C., & Golub, G. H. (1994). Inexact and preconditioned Uzawa algorithms for saddle point problems. en:SIAM Journal on Numerical Analysis, 31(6), 1645-1661.
  • Golub, G. H., Milanfar, P., & Varah, J. (1999). A stable numerical method for inverting shape from moments. en:SIAM Journal on Scientific Computing, 21(4), 1222-1243.

2000年代[編集]

  • Golub, G. H., Wu, X., & Yuan, J. Y. (2001). SOR-like methods for augmented systems. en:BIT Numerical Mathematics, 41(1), 71-85.
  • Benzi, M., Golub, G. H., & Liesen, J. (2005). Numerical solution of saddle point problems. en:Acta Numerica, 14, 1-137.
  • Beckermann, B., Golub, G. H., & Labahn, G. (2007). On the numerical condition of a generalized Hankel eigenvalue problem. en:Numerische Mathematik, 106(1), 41-68.
  • Bai, Z. Z., & Golub, G. H. (2007). Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. IMA Journal of Numerical Analysis, 27(1), 1-23.

関連項目[編集]

関連文献[編集]

  • Gautschi, W. (2002). The interplay between classical analysis and (numerical) linear algebra—a tribute to Gene H. Golub. Electron. Trans. Numer. Anal, 13, 119-147.
  • Trefethen, Lloyd N. (2007), "Obituary: Gene H. Golub (1932–2007)", Nature, 450 (7172): 962.
  • Chan, Raymond; Greif, Chen; O'Leary, Dianne (2007), Milestones in Matrix Computation: The selected works of Gene H. Golub with commentaries, Oxford University Press, ISBN 978-0-19-920681-0