Search Results - "Trefethen, Lloyd N."

The Exponentially Convergent Trapezoidal Rule by Trefethen, Lloyd N., Weideman, J. A. C.

“…It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics…”
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Representation of conformal maps by rational functions by Gopal, Abinand, Trefethen, Lloyd N.

“…The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated…”
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Numerical analytic continuation by Trefethen, Lloyd N.

“…Let f be an analytic function on a simply-connected compact continuum E of the complex z -plane. This might be an interval of the real line, where f might be…”
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AAA interpolation of equispaced data by Huybrechs, Daan, Trefethen, Lloyd N.

“…We propose AAA rational approximation as a method for interpolating or approximating smooth functions from equispaced samples. Although it is always better to…”
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Exponential node clustering at singularities for rational approximation, quadrature, and PDEs by Trefethen, Lloyd N., Nakatsukasa, Yuji, Weideman, J. A. C.

“…Rational approximations of functions with singularities can converge at a root-exponential rate if the poles are exponentially clustered. We begin by reviewing…”
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Is Gauss Quadrature Better than Clenshaw-Curtis? by Trefethen, Lloyd N.

“…We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw-Curtis. Seven-line MATLAB codes are presented that implement…”
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Multivariate polynomial approximation in the hypercube by TREFETHEN, LLOYD N.

“…Euclidean degree, defined in terms of the 2-norm rather than the 1-norm of the exponent vector \mathbf {k} of a monomial x_1^{k_1}\cdots \kern .8pt…”
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Chebfun and numerical quadrature by Hale, Nicholas, Trefethen, Lloyd N.

“…Chebfun is a Matlab-based software system that overloads Matlab’s discrete operations for vectors and matrices to analogous continuous operations for functions…”
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Numerical Conformal Mapping with Rational Functions by Trefethen, Lloyd N.

“…New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting…”
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Quantifying the ill-conditioning of analytic continuation by Trefethen, Lloyd N.

“…Analytic continuation is ill-posed, but becomes merely ill-conditioned (although with an infinite condition number) if it is known that the function in…”
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New Laplace and Helmholtz solvers by Gopal, Abinand, Trefethen, Lloyd N.

“…Numerical algorithms based on rational functions are introduced that solve the Laplace and Helmholtz equations on 2D domains with corners quickly and…”
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Continuous analogues of matrix factorizations by Townsend, Alex, Trefethen, Lloyd N.

“…Analogues of singular value decomposition (SVD), QR, LU and Cholesky factorizations are presented for problems in which the usual discrete matrix is replaced…”
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Computing the Gamma Function Using Contour Integrals and Rational Approximations by Schmelzer, Thomas, Trefethen, Lloyd N.

“…Some of the best methods for computing the gamma function are based on numerical evaluation of Hankel's contour integral. For example, Temme evaluates this…”
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Rectangular eigenvalue problems by Hashemi, Behnam, Nakatsukasa, Yuji, Trefethen, Lloyd N.

“…Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled…”
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NUMERICAL ALGORITHMS BASED ON ANALYTIC FUNCTION VALUES AT ROOTS OF UNITY by AUSTIN, ANTHONY P., KRAVANJA, PETER, TREFETHEN, LLOYD N.

“…Let f(z) be an analytic or meromorphic function in the closed unit disk sampled at the nth roots of unity. Based on these data, how can we approximately…”
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Barycentric Lagrange Interpolation by Berrut, Jean-Paul, Trefethen, Lloyd N.

“…Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of…”
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Hydrodynamic Stability Without Eigenvalues by Trefethen, Lloyd N., Trefethen, Anne E., Reddy, Satish C., Driscoll, Tobin A.

“…Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by…”
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Wave packet pseudomodes of variable coefficient differential operators by Trefethen, Lloyd N

“…-pseudoeigenfunctions of such operators for exponentially small values of…”
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A trapezoidal rule error bound unifying the Euler-Maclaurin formula and geometric convergence for periodic functions by Javed, Mohsin, Trefethen, Lloyd N.

“…The error in the trapezoidal rule quadrature formula can be attributed to discretization in the interior and non-periodicity at the boundary. Using a contour…”
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COMPUTING Aα, log( A ), AND RELATED MATRIX FUNCTIONS BY CONTOUR INTEGRALS by HALE, NICHOLAS, HIGHAM, NICHOLAS J., TREFETHEN, LLOYD N.

“…New methods are proposed for the numerical evaluation of f(A) or f(A)b, where f(A) is a function such as A 1/2 or log(A) with singularities in (—∞, 0] and A is…”
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