リチャード・バルガのソースを表示

'''リチャード・バルガ'''（Richard S. Varga、[[1928年]][[10月9日]]<ref name="mactutor">[http://mathshistory.st-andrews.ac.uk/Biographies/Varga.html MacTutor History of Mathematics archive]</ref> - [[2022年]][[2月25日]]）は、[[数値解析]]・[[数値線形代数]]・[[反復法 (数値計算)|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 (オハイオ州)|クリーブランド]]出身<ref name="mactutor"/>。

==著書==
* Varga, R. S. (1962). Iterative analysis. Prentice Hall, Englewood Cliffs, NJ.
* Varga, R. S. (1971). [[関数解析学|Functional analysis]] and [[:en:approximation theory|approximation theory]] in numerical analysis. [[SIAM (学会)|SIAM]].
* Varga, R. S. (1990). Scientific Computations on Mathematical Problems and Conjectures. [[SIAM (学会)|SIAM]].
* Edrei, A., Saff, E. B., & Varga, R. S. (2006). Zeros of sections of [[ベキ級数|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. [[:en:Springer Science & Business Media|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行列|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 [[SOR法|successive overrelaxation method]] and semi-iterative methods using [[チェビシェフ多項式|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 <math>||A^{-1}||_\infty</math>. 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.
* [[:en:Garrett Birkhoff|Birkhoff, G.]], & Varga, R. S. (1958). Reactor criticality and nonnegative matrices. Journal of the Society for Industrial and Applied Mathematics, 6(4), 354-377.
* [[:en:Garrett Birkhoff|Birkhoff, G.]], & Varga, R. S. (1959). Implicit alternating direction methods. Transactions of the American Mathematical Society, 92(1), 13-24.
====1960年代====
* [[ジーン・ゴラブ|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.
* [[:en:Garrett Birkhoff|Birkhoff, G.]], Varga, R. S., & Young, D. (1962). Alternating direction implicit methods. In Advances in computers (Vol. 3, pp. 189-273). [[エルゼビア|Elsevier]].
* [[:en:Garrett Birkhoff|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.
* [[:en:Garrett Birkhoff|Birkhoff, G.]], Schultz, M. H., & Varga, R. S. (1968). Piecewise [[:en:Hermite interpolation|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====
* [[:en:Walter Gautschi|Gautschi, W.]], & Varga, R. S. (1983). Error bounds for [[ガウス求積|Gaussian quadrature]] of [[解析関数|analytic functions]]. SIAM Journal on Numerical Analysis, 20(6), 1170-1186.
* Niethammer, W., & Varga, R. S. (1983). The analysis of <math>k</math>-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 [[リーマン予想|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 <math>\Lambda</math>, and the [[リーマン予想|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 <math>\cos(z)</math> and <math>\sin(z)</math> I. Numerical Algorithms, 25(1-4), 363-375.
* Varga, R. S., & Carpenter, A. J. (2001). Zeros of the partial sums of <math>\cos(z)</math> and <math>\sin(z)</math> 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)<ref>Varga, R. S. (1954). Properties of a special set of entire functions and their respective partial sums (Doctoral dissertation, Harvard University).</ref>

==出典==
{{reflist}}

==外部リンク==
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