ジーン・ゴラブ

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

• Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms, Gene H. Golub, Published by Springer-Verlag (1991) ISBN 0387523006 ISBN 13: 9780387523002
• Matrix Computations, Gene H. Golub, Published by North Oxford Academic (1983) ISBN 0946536058 ISBN 13: 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 13: 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 13: 9780801830112
• Scientific Computing: An Introduction with Parallel Computing, James M. Ortega; Gene H. Golub, Published by Elsevier Science & Technology Books, ISBN 0122892534 ISBN 13: 9780122892530
• Studies in Numerical Analysis. Studies in Mathematics, Volume 24, Golub, Gene H., editor, Published by Mathematical Association of America (1984) ISBN 0883851261 ISBN 13: 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 13: 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 13: 9780122083600

代表的な論文

単著

• Golub, G. (1965). Numerical methods for solving linear least squares problems. en:Numerische Mathematik, 7(3), 206-216.

共著

1960年代

• 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

• 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

• 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

• 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

• 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

• SIAM (学会)-1985/1986年に代表を務める
• EASIAM-過去に招待講演を行っている

関連文献

• 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

外部リンク

• ジーン・ゴラブ - Mathematics Genealogy Project
• Gene H Golub Memorial page
• Gene Golub, Oral history interview by Thomas Haigh
• Gene Golub in pictures around the world