ウォルター・ゴーチ
From Wikipedia, the free encyclopedia
- Numerical analysis: an introduction, Birkhäuser, Boston, 1997; 2nd edition, 2012.
- Orthogonal polynomials: computation and approximation, en:Oxford University Press, Oxford, 2004.
- Walter Gautschi, Selected Works with Commentaries, Springer Science & Business Media, 2013, 3 vols., Brezinski, Claude, and Ahmed Sameh, eds. volume 1; volume 2; volume 3.
- Orthogonal polynomials in MATLAB: exercises and solutions, SIAM, Philadelphia, 2016.
解説記事
- Gander, W., & Gautschi, W. (2000). Adaptive quadrature—revisited. en:BIT Numerical Mathematics, 40(1), 84-101.
- Gautschi, W. (1996). Orthogonal polynomials: applications and computation. en:Acta Numerica, 5, 45-119.
- Gautschi, W. (1981). A survey of Gauss-Christoffel quadrature formulae. In EB Christoffel (pp. 72-147). Birkhäuser, Basel.
- Gautschi, W. (1967). Computational aspects of three-term recurrence relations. SIAM Review, 9(1), 24-82.
代表的な論文
単著
- Gautschi, W. (1959). Some elementary inequalities relating to the gamma and incomplete gamma function. Journal of Mathematics and Physics, 38(1-4), 77-81.
- Gautschi, W. (1961). Numerical integration of ordinary differential equations based on trigonometric polynomials. en:Numerische Mathematik, 3(1), 381-397.
- Gautschi, W. (1962). On inverses of Vandermonde and confluent Vandermonde matrices. en:Numerische Mathematik, 4(1), 117-123.
- Gautschi, W. (1968). Construction of Gauss-Christoffel quadrature formulas. Math. Comp, 22(102), 251-270.
- Gautschi, W. (1970). Efficient computation of the complex error function. en:SIAM Journal on Numerical Analysis, 7(1), 187-198.
- Gautschi, W. (1970). On the construction of Gaussian quadrature rules from modified moments. en:Mathematics of Computation, 24(110), 245-260.
- Gautschi, W. (1982). On generating orthogonal polynomials. SIAM Journal on Scientific and Statistical Computing, 3(3), 289-317.
- Gautschi, W. (1994). Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Transactions on Mathematical Software (TOMS), 20(1), 21-62.
共著
- Gautschi, W., & Varga, R. S. (1983). Error bounds for Gaussian quadrature of analytic functions. en:SIAM Journal on Numerical Analysis, 20(6), 1170-1186.
- Flury, B. N., & Gautschi, W. (1986). An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form. SIAM Journal on Scientific and Statistical Computing, 7(1), 169-184.
- Gautschi, W., & Inglese, G. (1987). Lower bounds for the condition number of Vandermonde matrices. en:Numerische Mathematik, 52(3), 241-250.
