ニック・トレフェセン

ニック・トレフェセン (L. N. Trefethen, 1955年 8月30日 -) はイギリスの数学者。数値解析 (特に数値線形代数・常微分方程式の数値解法・偏微分方程式の数値解法^[1])などを専門とする。アメリカ合衆国ボストン生まれ。

著書

Trefethen, L. N., & Bau III, D. (1997). Numerical linear algebra. SIAM.
Trefethen, L. N. (2000). Spectral methods in MATLAB. SIAM.
Driscoll, T. A., & Trefethen, L. N. (2002). Schwarz-christoffel mapping (Vol. 8). en:Cambridge University Press.
Trefethen, L. N., & Embree, M. (2005). Spectra and pseudospectra: the behavior of nonnormal matrices and operators. en:Princeton University Press.
Trefethen, L. N. (2011). Trefethen's Index Cards: Forty Years of Notes about People, Words and Mathematics. en:World Scientific.
Trefethen, L. N. (2013). Approximation theory and approximation p. SIAM.
Trefethen, L. N., Birkisson, A., & Driscoll, T. A. (2017). Exploring ODEs. SIAM.

Numerical computation of the Schwarz–Christoffel transformation, LN Trefethen - SIAM Journal on Scientific and Statistical Computing, 1980.
Group velocity in finite difference schemes, LN Trefethen - SIAM Review, 1982.
Computation of pseudospectra, LN Trefethen - en:Acta Numerica, 1999.
Is Gauss quadrature better than Clenshaw–Curtis? LN Trefethen - SIAM Review, 2008.
Trefethen, L. N. (2015). Computing numerically with functions instead of numbers. Communications of the ACM, 58(10), 91-97.

Well-posedness of one-way wave equations and absorbing boundary conditions, LN Trefethen, L Halpern - en:Mathematics of Computation, 1986.

How fast are nonsymmetric matrix iterations? NM Nachtigal, SC Reddy, LN Trefethen - en:SIAM Journal on Matrix Analysis and Applications, 1992.
Hydrodynamic stability without eigenvalues, LN Trefethen, AE Trefethen, SC Reddy, TA Driscoll - Science, 1993.
Pseudospectra of linear operators, LN Trefethen - SIAM review, 1997.

Battles, Z., & Trefethen, L. N. (2004). An extension of MATLAB to continuous functions and operators. en:SIAM Journal on Scientific Computing, 25(5), 1743-1770.
Berrut, J. P., & Trefethen, L. N. (2004). Barycentric Lagrange interpolation. SIAM Review, 46(3), 501-517.
Kassam, A. K., & Trefethen, L. N. (2005). Fourth-order time-stepping for stiff PDEs. en:SIAM Journal on Scientific Computing, 26(4), 1214-1233.

The exponentially convergent trapezoidal rule, LN Trefethen, JAC Weideman - SIAM Review, 2014.
Townsend, A., & Trefethen, L. N. (2015). Continuous analogues of matrix factorizations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2173).
Trefethen, L. N. (2017). Cubature, approximation, and isotropy in the hypercube. SIAM Review, 59(3), 469-491.
Nakatsukasa, Y., Sète, O., & Trefethen, L. N. (2018). The AAA algorithm for rational approximation. en:SIAM Journal on Scientific Computing, 40(3), A1494-A1522.

Banjai, Lehel. (2003). Computation of conformal maps by fast multipole method accelerated Schwarz-Christoffel transformation (PhD thesis). University of Oxford.
Pachon, Ricardo (2010). Algorithms for polynomial and rational approximation (PhD thesis). University of Oxford.
Birkisson, Asgeir (2013). Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework (PhD thesis). University of Oxford.
Townsend, Alex (2014). Computing with functions in two dimensions (PhD thesis). University of Oxford.

^ Trefethen, L. N. (1996). Finite difference and spectral methods for ordinary and partial differential equations.
^ Driscoll, T. A., Hale, N., & Trefethen, L. N. (2014). Chebfun guide.
^ Platte, R. B., & Trefethen, L. N. (2010). Chebfun: a new kind of numerical computing. In Progress in industrial mathematics at ECMI 2008 (pp. 69-87). Springer, Berlin, Heidelberg.
^ "Wave Propagation and Stability for Finite Difference Schemes" supervised by Joseph E. Oliger at Stanford University.

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