リチャード・バルガ

リチャード・バルガは、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
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Varga, R. S. . Iterative analysis. Prentice Hall, Englewood Cliffs, NJ.
Varga, R. S. . Functional analysis and approximation theory in numerical analysis. SIAM.
Varga, R. S. . Scientific Computations on Mathematical Problems and Conjectures. SIAM.
Edrei, A., Saff, E. B., & Varga, R. S. . Zeros of sections of power series. Springer.
Graves-Morris, P. R., Saff, E. B., & Varga, R. S. . . Rational Approximation and Interpolation: Proceedings of the United Kingdom-United States Conference, Held at Tampa, Florida, December 12-16, 1983 . Springer.
Varga, R. S. . Geršgorin and his circles. Springer Science & Business Media. 

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

3. 代表的な論文
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3.1. 単著
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3.1.1. 1950年代
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Varga, R. S. . A comparison of the successive overrelaxation method and semi-iterative methods using Chebyshev polynomials. Journal of the Society for Industrial and Applied Mathematics, 5, 39-46.
Varga, R. S. . Factorization and normalized iterative methods . Westinghouse Electric Corp. Bettis Plant, Pittsburgh.

3.1.2. 1960年代
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Varga, R. S. . On higher order stable implicit methods for solving parabolic partial differential equations. Journal of Mathematics and Physics, 40, 220-231.
Varga, R. S. . Minimal Gerschgorin sets. Pacific Journal of Mathematics, 15, 719-729.
Varga, R. S. . On a discrete maximum principle. :en:SIAM Journal on Numerical Analysis, 3, 355-359.

3.1.3. 1970年代
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Varga, R. S. . On recurring theorems on diagonal dominance. Linear Algebra and its Applications, 13, 1-9.
Varga, R. S. . On diagonal dominance arguments for bounding . Linear Algebra and its applications, 14, 211-217.

3.2. 共著
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3.2.1. 1950年代
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Holladay, J. C., & Varga, R. S. . On powers of non-negative matrices. Proceedings of the American Mathematical Society, 9, 631-634.
Birkhoff, G., & Varga, R. S. . Reactor criticality and nonnegative matrices. Journal of the Society for Industrial and Applied Mathematics, 6, 354-377.
Birkhoff, G., & Varga, R. S. . Implicit alternating direction methods. Transactions of the American Mathematical Society, 92, 13-24.

3.2.2. 1960年代
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Golub, G. H., & Varga, R. S. . Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. :en:Numerische Mathematik, 3, 157-168.
Feingold, D. G., & Varga, R. S. . Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem. Pacific Journal of Mathematics, 12, 1241-1250.
Birkhoff, G., Varga, R. S., & Young, D. . Alternating direction implicit methods. In Advances in computers . Elsevier.
Birkhoff, G., & Varga, R. S. . Discretization errors for well-set Cauchy problems. J. Math. Phys, 44, 158.
Price, H. S., Varga, R. S., & Warren, J. E. . Application of oscillation matrices to diffusion‐convection equations. Journal of Mathematics and Physics, 45, 301-311.
Schultz, M. H., & Varga, R. S. . L-splines. :en:Numerische Mathematik, 10, 345-369.
Birkhoff, G., Schultz, M. H., & Varga, R. S. . Piecewise Hermite interpolation in one and two variables with applications to partial differential equations. :en:Numerische Mathematik, 11, 232-256.
Swartz, B. K., & Varga, R. S. . Error bounds for spline and L-spline interpolation. Journal of Approximation Theory, 6, 6-49.

3.2.3. 1980年代
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Gautschi, W., & Varga, R. S. . Error bounds for Gaussian quadrature of analytic functions. SIAM Journal on Numerical Analysis, 20, 1170-1186.
Niethammer, W., & Varga, R. S. . The analysis of -step iterative methods for linear systems from summability theory. :en:Numerische Mathematik, 41, 177-206.
Eiermann, M., Niethammer, W., & Varga, R. S. . A study of semiiterative methods for nonsymmetric systems of linear equations. :en:Numerische Mathematik, 47, 505-533.

3.2.4. 1990年代
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Csordas, G., & Varga, R. S. . Necessary and sufficient conditions and the Riemann hypothesis. Adv. in Appl. Math, 11, 328-357.
Starke, G., & Varga, R. S. . A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations. :en:Numerische Mathematik, 64, 213-240.
Eiermann, M., & Varga, R. S. . Zeros and local extreme points of Faber polynomials associated with hypocycloidal domains. Electron. Trans. Numer. Anal, 1, 49-71.
Nabben, R., & Varga, R. S. . 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, 107-113.
Csordas, G., Smith, W., & Varga, R. S. . Lehmer pairs of zeros, the de Bruijn-Newman constant , and the Riemann Hypothesis. Constructive Approximation, 10, 107-129.
Pritsker, I., & Varga, R. . The Szego curve, zero distribution and weighted approximation. Transactions of the American Mathematical Society, 349, 4085-4105.
Varga, R. S., & Krautstengl, A. . On Geršgorin-type problems and ovals of Cassini. Electron. Trans. Numer. Anal, 8, 15-20.

3.2.5. 2000年代
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Varga, R. S., & Carpenter, A. J. . Zeros of the partial sums of and I. Numerical Algorithms, 25, 363-375.
Varga, R. S., & Carpenter, A. J. . Zeros of the partial sums of and II. :en:Numerische Mathematik, 90, 371-400.
Cvetkovic, L., Kostic, V., & Varga, R. S. . A new Geršgorin-type eigenvalue inclusion set. Electron. Trans. Numer. Anal, 18, 73-80.
Varga, R. S., Cvetkovic, L., & Kostic, V. . 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. . Geršgorin‐type localizations of generalized eigenvalues. Numerical Linear Algebra with Applications, 16, 883-898.

4. 関連項目
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ハーバード大学 

5. 出典
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6. 外部リンク
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