Nick Trefethen | Academic Influence

Nick Trefethen's AcademicInfluence.com Rankings

Nick Trefethen

Mathematics

#2125

World Rank

#3328

Historical Rank

#849

USA Rank

Applied Mathematics

#89

World Rank

#102

Historical Rank

#45

USA Rank

Measure Theory

#518

World Rank

#731

Historical Rank

#210

USA Rank

mathematics Degrees

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Mathematics

Nick Trefethen's Degrees

PhD Mathematics Stanford University

Why Is Nick Trefethen Influential?

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According to Wikipedia, Lloyd Nicholas Trefethen is an American mathematician, professor of numerical analysis and head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford. Education Trefethen was born 30 August 1955 in Boston, Massachusetts, the son of mechanical engineer Lloyd M. Trefethen and codebreaker, poet, teacher and editor Florence Newman Trefethen. Trefethen attended Phillips Exeter Academy.

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Nick Trefethen's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Spectral Methods in MATLAB (2000) (3696)
Numerical linear algebra (1997) (1672)
Hydrodynamic Stability Without Eigenvalues (1993) (1605)
Spectra and pseudospectra : the behavior of nonnormal matrices and operators (2005) (1178)
Barycentric Lagrange Interpolation (2004) (1072)
Fourth-Order Time-Stepping for Stiff PDEs (2005) (868)
Spectra and Pseudospectra (2020) (753)
Is Gauss Quadrature Better than Clenshaw-Curtis? (2008) (616)
Pseudospectra of Linear Operators (1997) (515)
Group velocity in finite difference schemes (1981) (479)
The Exponentially Convergent Trapezoidal Rule (2014) (395)
How Fast are Nonsymmetric Matrix Iterations? (1992) (375)
Numerical computation of the Schwarz-Christoffel transformation (1979) (281)
Computation of pseudospectra (1999) (235)
An Extension of MATLAB to Continuous Functions and Operators (2004) (235)
Parabolic and hyperbolic contours for computing the Bromwich integral (2007) (231)
Well-Posedness of one-way wave equations and absorbing boundary conditions (1986) (216)
Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations (1996) (209)
The AAA Algorithm for Rational Approximation (2016) (201)
Talbot quadratures and rational approximations (2006) (200)
Linearized pipe flow to Reynolds number 10 7 (2003) (199)
Eigenvalues and pseudo-eigenvalues of Toeplitz matrices (1992) (186)
Wide-angle one-way wave equations. (1988) (156)
A Hybrid GMRES Algorithm for Nonsymmetric Linear Systems (1992) (156)
Average-case stability of Gaussian elimination (1990) (156)
Reviving the Method of Particular Solutions (2005) (154)
Low-dimensional models of subcritical transition to turbulence (1997) (143)
A mostly linear model of transition to tur (1995) (139)
Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples (2011) (137)
Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals (2008) (136)
Approximation theory and numerical linear algebra (1990) (133)
Is Gauss Quadrature Better than Clenshaw–Curtis? | SIAM Review | Vol. 50, No. 1 | Society for Industrial and Applied Mathematics (2008) (129)
Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals (2007) (124)
A Rational Spectral Collocation Method with Adaptively Transformed Chebyshev Grid Points (2006) (124)
Pseudozeros of polynomials and pseudospectra of companion matrices (1994) (123)
An Instability Phenomenon in Spectral Methods (1987) (122)
An Extension of Chebfun to Two Dimensions (2013) (121)
From Potential Theory to Matrix Iterations in Six Steps (1998) (120)
THE EIGENVALUES OF SECOND-ORDER SPECTRAL DIFFERENTIATION MATRICES* (1988) (116)
Robust Padé Approximation via SVD (2013) (109)
Group velocity interpretation of the stability theory of Gustafsson, Kreiss, and Sundström (1983) (109)
Large-Scale Computation of Pseudospectra Using ARPACK and Eigs (2001) (105)
Pseudospectra of the Convection-Diffusion Operator (1993) (103)
Stability of the method of lines (1992) (100)
Approximation Theory and Approximation Practice (Other Titles in Applied Mathematics) (2012) (99)
Approximation Theory and Approximation Practice, Extended Edition (2019) (97)
GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems (2018) (96)
The chebop system for automatic solution of differential equations (2008) (96)
Numerical conformal mapping (1986) (95)
Calculation of Pseudospectra by the Arnoldi Iteration (1996) (91)
Barycentric-Remez algorithms for best polynomial approximation in the chebfun system (2009) (85)
Rational Chebyshev approximation on the unit disk (1980) (82)
Two results on polynomial interpolation in equally spaced points (1991) (81)
The Carathéodory–Fejér Method for Real Rational Approximation (1983) (79)
Instability of difference models for hyperbolic initial boundary value problems (1984) (79)
Computed eigenmodes of planar regions (2005) (78)
Near-circularity of the error curve in complex Chebyshev approximation (1981) (77)
Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues (1990) (76)
Multivariate polynomial approximation in the hypercube (2016) (74)
On the resolvent condition in the Kreiss Matrix Theorem (1984) (72)
Continuous analogues of matrix factorizations (2015) (69)
Robust rational interpolation and least-squares (2011) (69)
New Quadrature Formulas from Conformal Maps (2008) (68)
A Modified Schwarz-Christoffel Transformation for Elongated Regions (1990) (67)
Numerical Algorithms Based on Analytic Function Values at Roots of Unity (2014) (64)
Computing Numerically with Functions Instead of Numbers (2007) (63)
Chebfun: A New Kind of Numerical Computing (2010) (59)
The kink phenomenon in Fejér and Clenshaw–Curtis quadrature (2007) (59)
Condition Numbers of Random Triangular Matrices (1996) (57)
Piecewise smooth chebfuns (2010) (56)
Analysis and design of polygonal resistors by conformal mapping (1984) (55)
Green's Functions for Multiply Connected Domains via Conformal Mapping (1999) (55)
Conformal mapping solution of Laplace's equation on a polygon with oblique derivative boundary conditions (1986) (54)
Stiffness of ODEs (1993) (54)
MultiMATLAB: MATLAB on Multiple Processors (1996) (54)
Growth and decay of random Fibonacci sequences (1999) (54)
Extension of Chebfun to Periodic Functions (2015) (51)
Householder triangularization of a quasimatrix (2010) (49)
Computing the Gamma Function Using Contour Integrals and Rational Approximations (2007) (48)
From the Buffon Needle Problem to the Kreiss Matrix Theorem (1994) (47)
Generalizing Eigenvalue Theorems to Pseudospectra Theorems (2001) (47)
Computing Eigenvalues of Real Symmetric Matrices with Rational Filters in Real Arithmetic (2015) (45)
Rational Minimax Approximation via Adaptive Barycentric Representations (2017) (45)
The Chebyshev Polynomials of a Matrix (1999) (45)
Mathematics of the Faraday Cage (2015) (42)
Cubature, Approximation, and Isotropy in the Hypercube (2017) (42)
Six myths of polynomial interpolation and quadrature (2011) (41)
Spectra and pseudospectra for pipe Poiseuille flow (1999) (41)
How many shuffles to randomize a deck of cards? (2000) (40)
Chebfun in Three Dimensions (2017) (39)
The Kreiss Matrix Theorem on a General Complex Domain (1999) (38)
Spectra, pseudospectra, and localization for random bidiagonal matrices (2000) (37)
Classical free-streamline flow over a polygonal obstacle (1986) (36)
The asymptotic accuracy of rational best approximations to ez on a disk (1984) (36)
Wave packet pseudomodes of twisted Toeplitz matrices (2004) (36)
Chopping a Chebyshev Series (2015) (36)
The CF table (1990) (34)
A New Direction in Hydrodynamic Stability: Beyond Eigenvalues (1992) (34)
Real Polynomial Chebyshev Approximation by the Carathéodory–Fejér method (1982) (34)
Pseudospectra for the wave equation with an absorbing boundary (1996) (34)
Schwarz-Christoffel mapping in the computer era. (1998) (34)
The Definition of Numerical Analysis (1992) (33)
Ideal jet flow in two dimensions (1987) (32)
Solving Laplace Problems with Corner Singularities via Rational Functions (2019) (32)
Stability of Barycentric Interpolation Formulas for Extrapolation (2012) (31)
The Carathéodory-Fejér method for recursive digital filter design (1983) (30)
Pseudospectra of rectangular matrices (2002) (30)
Chebfun and numerical quadrature (2012) (30)
Stability of finite difference models containing two boundaries or interfaces (1985) (30)
A Multipole Method for Schwarz-Christoffel Mapping of Polygons with Thousands of Sides (2003) (30)
Smooth Random Functions, Random ODEs, and Gaussian Processes (2019) (28)
Fourier Analysis of the SOR Iteration (1988) (27)
Block Operators and Spectral Discretizations (2017) (26)
Exploring ODEs (2018) (26)
Vandermonde with Arnoldi (2019) (25)
A Sinc Function Analogue of Chebfun (2011) (25)
Computation of conformal maps by modified schwarz-christoffel transformations (1990) (25)
Representation of conformal maps by rational functions (2018) (25)
A spectral Petrov-Galerkin formulation for pipe flow I: Linear stability and transient growth (2000) (25)
Computing Yapunov constants for random recurrences with smooth coefficients (2001) (25)
Ten Digit Algorithms (2005) (24)
Chebyshev Approximation on the Unit Disk (1983) (23)
Three mysteries of Gaussian elimination (1985) (22)
Numerical Conformal Mapping with Rational Functions (2019) (22)
Wave propagation and stability for finite difference schemes (1982) (22)
Wave packet pseudomodes of variable coefficient differential operators (2005) (21)
A trapezoidal rule error bound unifying the Euler–Maclaurin formula and geometric convergence for periodic functions (2014) (21)
Quantifying the ill-conditioning of analytic continuation (2019) (21)
Threshold amplitudes for transition to turbulence in a pipe (2000) (20)
Square blocks and equioscillation in the Padé, walsh, and cf tables (1984) (20)
A robust implementation of the Carathéodory-Fejér method for rational approximation (2011) (19)
New Laplace and Helmholtz solvers (2019) (19)
An algorithm for real and complex rational minimax approximation (2019) (18)
Exactness of quadrature formulas (2021) (18)
Exponential node clustering at singularities for rational approximation, quadrature, and PDEs (2020) (18)
Nonuniqueness of best rational Chebyshev approximations on the unit disk (1983) (18)
Large‐amplitude transient growth in the linear evolution of equatorial spread F with a sheared zonal flow (1999) (17)
SERIES SOLUTION OF LAPLACE PROBLEMS (2018) (17)
III‐posedness of absorbing boundary conditions for migration (1988) (16)
Do the Pseudospectra of a Matrix Determine its Behavior (1993) (16)
Computing numerically with functions instead of numbers (2015) (16)
Gaussian elimination as an iterative algorithm (2013) (15)
Real and complex Chebyshev approximation on the unit disk and interval (1983) (14)
On Convergence and Degeneracy in Rational Padé and Chebyshev Approximation (1985) (14)
Eigenvalues and musical instraments (2001) (13)
A spectral Petrov-Galerkin formulation for pipe flow II: Nonlinear transitional stages (2001) (13)
Pade´, stable Pade´, and Chebyshev-Pade´ approximation (1987) (12)
Trigonometric Interpolation and Quadrature in Perturbed Points (2016) (12)
Erratum: Numerical Computation of the Schwarz–Christoffel Transformation (1980) (11)
Computations of Eigenvalue Avoidance in Planar Domains (2004) (11)
Predictions for Scientific Computing Fifty Years from Now (1998) (9)
Circularity of the Error Curve and Sharpness of the CF Method in Complex Chebyshev Approximation (1983) (9)
Pseudospectra of the Linear Navier-Stokes Evolution Operator and Instability of Plane Poiseuille and Couette Flows: (preliminary report) (1992) (9)
Euler–Maclaurin and Gregory interpolants (2016) (9)
FINITE DIFFERENCE AND SPECTRAL METHODS FOR ORDINARY (1996) (9)
Piecewise Continuous Toeplitz Matrices and Operators: Slow Approach to Infinity (2002) (9)
Pseudospectra of the Wave Operator with an Absorbing Boundary (1993) (7)
REAL VS. COMPLEX RATIONAL CHEBYSHEV APPROXIMATION ON AN INTERVAL (1983) (7)
Eigenvalues and Pseudospectra of Rectangular Matrices (2001) (7)
Ten Digit Problems (2011) (7)
Lightning Stokes solver (2021) (7)
Schwarz–Christoffel Mapping: Introduction (2002) (7)
Schwarz-Christoffel Mapping in the 1980's (1993) (6)
Barycentric Lagrange Interpolation As discussed by Jean-Paul Berrut and (2014) (6)
AAA-least squares rational approximation and solution of Laplace problems (2021) (6)
A Numerical Analyst Looks at the "Cutoff Phenomenon" in Card Shuffling and Other Markov Chains (1997) (5)
Measurement of Mean Fluid Temperatures (1956) (5)
Four bugs on a rectangle (2011) (5)
Reciprocal-log approximation and planar PDE solvers (2020) (5)
COMPUTING COMPLEX SINGULARITIES OF DIFFERENTIAL EQUATIONS WITH CHEBFUN (2013) (5)
Rational approximation of $x^n$ (2018) (4)
Matrix Iterations: The Six Gaps Between Potential Theory and Convergence (1996) (4)
IV.21 Numerical Analysis (2010) (4)
1. Differentiation Matrices (2000) (4)
Rectangular eigenvalue problems (2021) (4)
Computing with functions in two dimensions (2014) (3)
LAX-STABILITY OF FULLY DISCRETE SPECTRAL METHODS VIA ST~ILITY REGIONS AND ~EU~-EIGE (1990) (3)
6. Chebyshev Differentiation Matrices (2000) (3)
Numerical Solution of the Omitted Area Problem of Univalent Function Theory (2001) (3)
Essentials of Schwarz–Christoffel mapping (2002) (3)
14. Fourth-Order Problems (2000) (3)
ASYMPTOTIC APPROACHES IN THE THEORY OF SHELLS: LONG HISTORY AND NEW TRENDS UDC 531.3 (2006) (3)
Log-lightning computation of capacity and Green's function (2021) (3)
Trefethen's Index Cards: Forty Years of Notes About People, Words and Mathematics (2011) (3)
Matrix Behaviour, Unitary Reducibility, and Hadamard Products (1996) (3)
Stability of barycentric interpolation formulas (2011) (3)
Computer Application of the Schwarz-Christoffel Transformation (1981) (3)
Real vs. Complex Rational Chebyshev Approximation on Complex Domains (1983) (3)
Fourier Analysis of Numerical Approximations of Hyperbolic Equations (R. Vichnevetsky and J. B. Bowles) (1984) (2)
Computing Lyapunov constants for random recurrences with smooth coe $ cients (2000) (2)
Inverse Yogiisms (2018) (2)
Appendix: The Definition of Numerical Analysis (1997) (2)
4. Smoothness and Spectral Accuracy (2000) (2)
Impossibility of approximating analytic functions from equispaced samples (2009) (2)
Advanced Problems: 6460-6462 (1984) (2)
The Remez algorithm for trigonometric approximation of periodic functions (2015) (2)
Obituary: Gene H. Golub (1932–2007) (2007) (2)
8. Chebyshev Series and the FFT (2000) (1)
REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS (1998) (1)
Conformal mapping and convergence of Krylov iterations (1994) (1)
Resolution of singularities by rational functions (2023) (1)
II QR Factorization and Least Squares (1997) (1)
2. Unbounded Grids: The Semidiscrete Fourier Transform (2000) (1)
Algorithms for polynomial and rational approximation (2010) (1)
AAA interpolation of equispaced data (2022) (1)
Iv. Branches of Mathematics Iv.21 Numerical Analysis (2008) (1)
IV Systems of Equations (1997) (1)
Rational approximation of 𝐱ⁿ (2018) (1)
Representation of conformal maps by rational functions (2019) (1)
How many shu es to randomize a deck ofcards ? (1999) (1)
5. Polynomial Interpolation and Clustered Grids (2000) (1)
Schwarz–Christoffel Mapping: Appendix: Using the SC Toolbox (2002) (1)
III Conditioning and Stability (1997) (1)
Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework (2013) (0)
Book Review: The Princeton Companion to Applied Mathematics (2016) (0)
Life and DNA (2011) (0)
Sigmoid functions and multiscale resolution of singularities (2023) (0)
Numerical Conformal Mapping and Applications (1989) (0)
A Bibliography of Publications of Lloyd Nicholas Trefethen (2014) (0)
Both Gauss – Legendre and Gauss – Chebyshev are special cases of Gauss – Jacobi (2012) (0)
Cold War Nukes (2011) (0)
Electronic Transactions on Numerical Analysis Volume 29, 2007–2008 Contents (2009) (0)
13. More about Boundary Conditions (2000) (0)
Writing and Literature (2011) (0)
The Meaning of Life (2011) (0)
Chebfun and numerical quadrature (2012) (0)
10. Time-Stepping and Stability Regions (2000) (0)
VI Iterative Methods (1997) (0)
Electronic EditionPseudozeros of polynomials and pseudospectraof companion matrices ? (1994) (0)
Quantifying the ill-conditioning of analytic continuation (2020) (0)
Politics and Society (2011) (0)
REAL VS. COMPLEX RATIONAL CHEBYSHEV APPROXIMATION (2016) (0)
Optimizing Your Life (2011) (0)
The Kreiss Matrix Theorem (2020) (0)
Convergence estimates for iterative methods via the Kriess Matrix Theorem on a general complex domain (1994) (0)
ON CONVERGENCEAND DEGENERACY IN RATIONALPADI AND CHEBYSHEVAPPROXIMATION (1985) (0)
7. Boundary Value Problems (2000) (0)
Living with Others (2011) (0)
11. Polar Coordinates (2000) (0)
SUPPLEMENTARY MATERIALS: PROOF OF THEOREM 2.1 (2017) (0)
Linear non-modal phenomena in numerical analysis and applied mathematics. First annual performance report, February 15, 1994--November 15, 1994 (1994) (0)
Good and Evil (2011) (0)
3. Periodic Grids: The DFT and FFT (2000) (0)
Mathematics and Science in Everyday Life (2011) (0)
BOOK REVIEW FOR BULLETIN OF THE AMS (2006) (0)
12. Integrals and Quadrature Formulas (2000) (0)
God and Religion (2011) (0)
Eight Perspectives on the Exponentially Ill-Conditioned Equation ε y" - x y' + y = 0 (2020) (0)
Aging and Death (2011) (0)
The Life of the Professor (2011) (0)
Stiiness of Odes (1993) (0)
Spectacularly Large Expansion Coefficients in Müntz’s Theorem (2022) (0)
Scientific Computing and the Chebfun System Case for Support Prof (2006) (0)
Schwarz–Christoffel Mapping: Numerical methods (2002) (0)
9. Eigenvalues and Pseudospectra (2000) (0)
X. Further Mathematical Issues (2005) (0)
Stars and Planets (2011) (0)
Chastened Challenge Sponsor: " I Misjudged " (0)
Number 12 / 22 Chebfun and Numerical Quadrature by (2012) (0)
Trefethen periodic functions Maclaurin formula and geometric convergence for − A trapezoidal rule error bound unifying the Euler (2013) (0)
Knowledge and Truth (2011) (0)
Euler–Maclaurin and Gregory interpolants (2015) (0)
Hearts Minds and Bodies (2011) (0)
Spectral Methods in MATLAB 62026th Edition (2001) (0)
Mat261 - Numerical Linear Algebra Curriculum Fall 2009 (2009) (0)

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Nick Trefethen has made the following academic contributions:

Numerical Linear Algebra