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^[1] - ）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^[1]。

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 ${\displaystyle ||A^{-1}||_{\infty }}$ . 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 ${\displaystyle k}$ -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 ${\displaystyle \Lambda }$ , 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 ${\displaystyle \cos(z)}$  and ${\displaystyle \sin(z)}$  I. Numerical Algorithms, 25(1-4), 363-375.
• Varga, R. S., & Carpenter, A. J. (2001). Zeros of the partial sums of ${\displaystyle \cos(z)}$  and ${\displaystyle \sin(z)}$  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)^[2]

出典

1. ^ ^{a b} MacTutor History of Mathematics archive
2. ^ Varga, R. S. (1954). Properties of a special set of entire functions and their respective partial sums (Doctoral dissertation, Harvard University).

外部リンク

• リチャード・バルガ - Mathematics Genealogy Project
• リチャード・バルガ - DBLP Bibliography Server