リチャード・バルガ

リチャード・バルガ（Richard S. Varga、1928年10月9日 - 2022年2月25日）は、数値解析・数値線形代数・反復法・行列解析・複素解析を専門とするアメリカ合衆国の数学者。オハイオ州クリーブランド出身。

著書
 Varga, R. S. (1962). Iterative analysis. Prentice Hall, Englewood Cliffs, NJ.
 Varga, R. S. (1971). Functional analysis and approximation theory in numerical analysis. SIAM.
 Varga, R. S. (1990). Scientific Computations on Mathematical Problems and Conjectures. SIAM.
 Edrei, A., Saff, E. B., & Varga, R. S. (2006). Zeros of sections of power series. Springer.
 Graves-Morris, P. R., Saff, E. B., & Varga, R. S. (Eds.). (2006). Rational Approximation and Interpolation: Proceedings of the United Kingdom-United States Conference, Held at Tampa, Florida, December 12-16, 1983 (Vol. 1105). Springer.
 Varga, R. S. (2010). Geršgorin and his circles. Springer Science & Business Media. (ゲルシュゴリンの定理に関する文献)

解説記事
 Varga, R. S. (1976). M-matrix theory and recent results in numerical linear algebra. In Sparse Matrix Computations (pp. 375-387). Academic Press.
 Varga, R. S. (1982). Topics in polynomial and rational interpolation and approximation. Montréal: Presses de l'Université de Montréal.
 Varga, R. S. (1986). Scientific computation on some mathematical conjectures. Approximation theory, 5, 191-209.
 Kincaid, D. R., Varga, R. S., & Warlick, C. H. (2010). The life and times of Dr David M. Young, Jr. Numerical Linear Algebra with Applications, 17(5), 743-757.

代表的な論文

単著

1950年代
 Varga, R. S. (1957). A comparison of the successive overrelaxation method and semi-iterative methods using Chebyshev polynomials. Journal of the Society for Industrial and Applied Mathematics, 5(2), 39-46.
 Varga, R. S. (1959). Factorization and normalized iterative methods (No. WAPD-T-950). Westinghouse Electric Corp. Bettis Plant, Pittsburgh.

1960年代
 Varga, R. S. (1961). On higher order stable implicit methods for solving parabolic partial differential equations. Journal of Mathematics and Physics, 40(1-4), 220-231.
 Varga, R. S. (1965). Minimal Gerschgorin sets. Pacific Journal of Mathematics, 15(2), 719-729.
 Varga, R. S. (1966). On a discrete maximum principle. :en:SIAM Journal on Numerical Analysis, 3(2), 355-359.

1970年代
 Varga, R. S. (1976). On recurring theorems on diagonal dominance. Linear Algebra and its Applications, 13(1-2), 1-9.
 Varga, R. S. (1976). On diagonal dominance arguments for bounding . Linear Algebra and its applications, 14(3), 211-217.

共著

1950年代
 Holladay, J. C., & Varga, R. S. (1958). On powers of non-negative matrices. Proceedings of the American Mathematical Society, 9(4), 631-634.
 Birkhoff, G., & Varga, R. S. (1958). Reactor criticality and nonnegative matrices. Journal of the Society for Industrial and Applied Mathematics, 6(4), 354-377.
 Birkhoff, G., & Varga, R. S. (1959). Implicit alternating direction methods. Transactions of the American Mathematical Society, 92(1), 13-24.

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.
 Feingold, D. G., & Varga, R. S. (1962). Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem. Pacific Journal of Mathematics, 12(4), 1241-1250.
 Birkhoff, G., Varga, R. S., & Young, D. (1962). Alternating direction implicit methods. In Advances in computers (Vol. 3, pp. 189-273). Elsevier.
 Birkhoff, G., & Varga, R. S. (1965). Discretization errors for well-set Cauchy problems. J. Math. Phys, 44(1-23), 158.
 Price, H. S., Varga, R. S., & Warren, J. E. (1966). Application of oscillation matrices to diffusion‐convection equations. Journal of Mathematics and Physics, 45(1-4), 301-311.
 Schultz, M. H., & Varga, R. S. (1967). L-splines. :en:Numerische Mathematik, 10(4), 345-369.
 Birkhoff, G., Schultz, M. H., & Varga, R. S. (1968). Piecewise Hermite interpolation in one and two variables with applications to partial differential equations. :en:Numerische Mathematik, 11(3), 232-256.
 Swartz, B. K., & Varga, R. S. (1972). Error bounds for spline and L-spline interpolation. Journal of Approximation Theory, 6(1), 6-49.

1980年代
 Gautschi, W., & Varga, R. S. (1983). Error bounds for Gaussian quadrature of analytic functions. SIAM Journal on Numerical Analysis, 20(6), 1170-1186.
 Niethammer, W., & Varga, R. S. (1983). The analysis of -step iterative methods for linear systems from summability theory. :en:Numerische Mathematik, 41(2), 177-206.
 Eiermann, M., Niethammer, W., & Varga, R. S. (1985). A study of semiiterative methods for nonsymmetric systems of linear equations. :en:Numerische Mathematik, 47(4), 505-533.

1990年代
 Csordas, G., & Varga, R. S. (1990). Necessary and sufficient conditions and the Riemann hypothesis. Adv. in Appl. Math, 11(3), 328-357.
 Starke, G., & Varga, R. S. (1993). A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations. :en:Numerische Mathematik, 64(1), 213-240.
 Eiermann, M., & Varga, R. S. (1993). Zeros and local extreme points of Faber polynomials associated with hypocycloidal domains. Electron. Trans. Numer. Anal, 1, 49-71.
 Nabben, R., & Varga, R. S. (1994). A linear algebra proof that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant Stieltjes matrix. :en:SIAM Journal on Matrix Analysis and Applications, 15(1), 107-113.
 Csordas, G., Smith, W., & Varga, R. S. (1994). Lehmer pairs of zeros, the de Bruijn-Newman constant , and the Riemann Hypothesis. Constructive Approximation, 10(1), 107-129.
 Pritsker, I., & Varga, R. (1997). The Szego curve, zero distribution and weighted approximation. Transactions of the American Mathematical Society, 349(10), 4085-4105.
 Varga, R. S., & Krautstengl, A. (1999). On Geršgorin-type problems and ovals of Cassini. Electron. Trans. Numer. Anal, 8, 15-20.

2000年代
 Varga, R. S., & Carpenter, A. J. (2000). Zeros of the partial sums of  and  I. Numerical Algorithms, 25(1-4), 363-375.
 Varga, R. S., & Carpenter, A. J. (2001). Zeros of the partial sums of  and  II. :en:Numerische Mathematik, 90(2), 371-400.
 Cvetkovic, L., Kostic, V., & Varga, R. S. (2004). A new Geršgorin-type eigenvalue inclusion set. Electron. Trans. Numer. Anal, 18, 73-80.
 Varga, R. S., Cvetkovic, L., & Kostic, V. (2008). Approximation of the minimal Geršgorin set of a square complex matrix. Electronic Transactions on Numerical Analysis, 30, 398-405.
 Kostić, V., Cvetković, L. J., & Varga, R. S. (2009). Geršgorin‐type localizations of generalized eigenvalues. Numerical Linear Algebra with Applications, 16(11‐12), 883-898.

関連項目
 ハーバード大学 (1954年に博士号を取得)

出典

外部リンク

数値解析
数値線形代数
線型代数学
複素解析
アメリカ合衆国の数学者
アメリカ合衆国の数値解析研究者
アメリカ数学会フェロー
ハーバード大学出身の人物
クリーブランド出身の人物
281009
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数学に関する記事
1928年生
2022年没