WorldCat Identities

Trefethen, Lloyd N. (Lloyd Nicholas)

Works: 80 works in 261 publications in 1 language and 5,309 library holdings
Genres: Quotations  Science films  Nonfiction films  Short films  Educational films  Documentary films  Internet videos  Miscellanea 
Roles: Author, Thesis advisor, Editor, Teacher , Opponent, Other
Classifications: QA300, 512.5
Publication Timeline
Most widely held works by Lloyd N Trefethen
Numerical linear algebra by Lloyd N Trefethen( Book )

26 editions published between 1997 and 2000 in English and Undetermined and held by 623 WorldCat member libraries worldwide

An introduction to the field of numerical linear algebra. It aims to present the core, standard material in a novel way. Topics include iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability
Spectra and pseudospectra : the behavior of nonnormal matrices and operators by Lloyd N Trefethen( Book )

11 editions published in 2005 in English and held by 388 WorldCat member libraries worldwide

"This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences."--Jacket
Spectral methods in MATLAB by Lloyd N Trefethen( Book )

21 editions published between 2000 and 2008 in English and held by 370 WorldCat member libraries worldwide

Mathematics of Computing -- Numerical Analysis
Schwarz-Christoffel mapping by Tobin A Driscoll( Book )

17 editions published in 2002 in English and held by 248 WorldCat member libraries worldwide

"This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and many applications in fields such as electromagnetism, fluid flow, design and inverse problems, and the solution of linear systems of equations. As a modern treatment of this subject, it is an accessible resource for engineers, scientists, and applied mathematicians who seek more experience with theoretical or computational conformal mapping techniques."--Jacket
Approximation theory and approximation practice by Lloyd N Trefethen( Book )

13 editions published between 2012 and 2013 in English and held by 198 WorldCat member libraries worldwide

Numerical conformal mapping by Lloyd N Trefethen( Book )

9 editions published between 1985 and 1986 in English and held by 102 WorldCat member libraries worldwide

A new direction in hydrodynamic stability : beyond Eigenvalues by Institute for Computer Applications in Science and Engineering( Book )

7 editions published in 1992 in English and Undetermined and held by 80 WorldCat member libraries worldwide

Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and looking for unstable eigenvalues of the linearized problem, but the results agree poorly in many cases with experiments. Nevertheless, it has become clear in recent years that linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis can be obtained by considering the pseudospectra of the linearized problem, which reveals that small perturbations to the smooth flow in the form of streamwise vortices may be amplified by factors on the order of 105 by a linear mechanism, even though all the eigenmodes are stable. The same principles apply also to other problems in the mathematical sciences that involve non-orthogonal eigenfunctions ... Hydrodynamic stability, Transition to turbulence
Stability of finite difference models containing two boundaries of interfaces by Lloyd N Trefethen( Book )

1 edition published in 1984 in English and held by 79 WorldCat member libraries worldwide

Fourier analysis of the SOR iteration by Randall J LeVeque( Book )

6 editions published in 1986 in English and held by 75 WorldCat member libraries worldwide

The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. We show that for the standard model problem of Poisson's equation on a rectangle, the optimal omega and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR Successive overrelaxation stencil becomes symmetrical. The tilted grid also gives insight into the relation between convergence rates of several variants. Keywords: Successive overrelaxation, Iterative methods
Classical free-streamline flow over a polygonal obstacle by Alan R Elcrat( Book )

3 editions published in 1984 in English and held by 72 WorldCat member libraries worldwide

Well-posedness of one-way wave equations and absorbing boundary conditions by Lloyd N Trefethen( Book )

4 editions published in 1985 in English and held by 70 WorldCat member libraries worldwide

Surface tension in fluid mechanics( Visual )

9 editions published between 1967 and 1988 in English and held by 67 WorldCat member libraries worldwide

Presents a series of experiments to show that surfaces exert forces. Defines the fundamental boundary conditons governing the effects of these forces. Includes illustrations of nucleation, "wine tears", swimming bubbles, and high-speed pictures of the breakup of water sheets and soap films
Fundamentals of complex analysis with applications to engineering and science by E. B Saff( Book )

6 editions published between 2003 and 2017 in English and held by 15 WorldCat member libraries worldwide

Wave propagation and stability for finite difference schemes by Lloyd N Trefethen( Book )

7 editions published in 1982 in English and Undetermined and held by 14 WorldCat member libraries worldwide

This dissertation investigates the behavior of finite difference models of linear hyperbolic partial differential equations. Whereas a hyperbolic equation is nondispersive and nondissipative, difference models are invariably dispersive, and often dissipative too. We set about analyzing them by means of existing techniques from the theory of dispersive wave propagation, making extensive use in particular of the concept of group velocity, the velocity at which energy propagates. The first three chapters present a general analysis of wave propagation in difference models. We describe systematically the effects of dispersion on numerical errors, for both smooth and parasitic waves. The reflection and transmission of waves at boundaries and interfaces are then studied at length. The key point for this is a distinction introduced here between leftgoing and rightgoing signals, which is based not on the characteristics of the original equation, but on the group velocities of the numerical model. The last three chapters examine stability for finite difference models of initial boundary value problems
Numerical Computation of the Schwarz-Christoffel Transformation by Lloyd N Trefethen( Book )

5 editions published in 1979 in English and held by 8 WorldCat member libraries worldwide

A program is described which computes Schwartz-Christoffel transformations that map the unit disk conformally onto the interior of a bounded or unbounded polygon in the complex plane. The inverse map is also computed. The computational problem is approached by setting up a nonlinear system of equations whose unknowns are essentially the accessory parameters z sub k. This system is then solved with a packaged subroutine. New features of this work include the evaluation of integrals within the disk rather than along the boundary, making possible the treatment of unbounded polygons; the use of a compound form of Gauss-Jacobi quadrature to evaluate the Schwarz-Christoffel integral, making possible high accuracy at reasonable cost; and the elimination of constraints in the nonlinear system by a simple change of variables. Schwarz-Christoffel transformations may be applied to solve the Laplace and Poisson equations and related problems in two-dimensional domains with irregular or unbounded (but not curved or multiply connected) geometries. Computational examples are presented. The time required to solve the mapping problem is roughly proportional to N-cubed, where N is the number of vertices of the polygon. A typical set of computations to 8-place accuracy with N <or = 10 takes 1 to 10 seconds on an IBM 370/168. (Author)
Pseudospectra of the convection-diffusion operator by S. C Reddy( Book )

3 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide

Abstract: "The spectrum of the simplest ID convection-diffusion operator is a discrete subset of the negative real axis, but the pseudospectra are regions in the complex plane that approximate parabolas. Put another way, the norm of the resolvent is exponentially large as a function of the Péclet number throughout a certain parabolic region. These observations have a simple physical basis, and suggest that conventional spectral analysis for convection-diffusion operators may be of limited value in some applications."
Trefethen's index cards : forty years of notes about people, words and mathematics by Lloyd N Trefethen( Book )

7 editions published in 2011 in English and Undetermined and held by 5 WorldCat member libraries worldwide

Acclaimed mathematician Lloyd N Trefethen, Professor of Numerical Analysis at Oxford University, has created an intellectual diary, marking the development of his interests and ideas, from his teenage years to the present. These thoughts stand as signposts, directing us through a mind that applies the same scientific discipline and rigor in everyday life as that needed for success in science and academia. Informative and entertaining, Professor Trefethen's Index Cards is a collage of observations of rare clarity, in subjects ranging from astronomy to family life, and from music to politics. The book will be of interest not only to other scientists and mathematicians, but to anyone in the general public interested in discerning how a scientific outlook informs the way we see broader issues in the societies we live in
Fundamentals of complex analysis for mathematics, science, and engineering by E. B Saff( Book )

3 editions published between 1993 and 2003 in English and held by 5 WorldCat member libraries worldwide

Special issue on numerical conformal mapping( Book )

2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide

Pseudospectra of linear operators by Lloyd N Trefethen( Book )

3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide

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Numerical linear algebra
Alternative Names
Lloyd N. Trefethen Amerikaans wiskundige

Lloyd N. Trefethen amerikansk matematikar

Lloyd N. Trefethen amerikansk matematiker

Lloyd N. Trefethen mathématicien américain

Lloyd Nicholas Trefethen

Lloyd Nicholas Trefethen US-amerikanischer Mathematiker

Trefethen, L. 1955-

Trefethen, L. N. 1955-

Trefethen, Lloyd 1955-

Trefethen, Lloyd N.

Trefethen, Lloyd Nicholas 1955-

Trefethen, N. 1955-

Trefethen, Nick

Trefethen, Nick 1955-


English (167)

Spectra and pseudospectra : the behavior of nonnormal matrices and operatorsSpectral methods in MATLABSchwarz-Christoffel mappingFundamentals of complex analysis with applications to engineering and scienceTrefethen's index cards : forty years of notes about people, words and mathematicsFundamentals of complex analysis for mathematics, science, and engineering