Trefethen, Lloyd N. (Lloyd Nicholas)
Overview
Works:  74 works in 254 publications in 1 language and 5,079 library holdings 

Genres:  Quotations Science films Nonfiction films Short films Educational films Documentary films Internet videos Miscellanea 
Roles:  Author, Thesis advisor, Editor, Teacher , Other 
Classifications:  QA300, 512.5 
Publication Timeline
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Most widely held works about
Lloyd N Trefethen
 Trefethen's index cards : forty years of notes about people, words and mathematics by Lloyd N Trefethen( Book )
 Trefethen, Lloyd Nicholas : numerical analysis( )
Most widely held works by
Lloyd N Trefethen
Numerical linear algebra by
Lloyd N Trefethen(
Book
)
23 editions published between 1997 and 2000 in English and held by 603 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
23 editions published between 1997 and 2000 in English and held by 603 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 383 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 selfcontained 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
11 editions published in 2005 in English and held by 383 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 selfcontained 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
)
20 editions published between 2000 and 2008 in English and held by 365 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
20 editions published between 2000 and 2008 in English and held by 365 WorldCat member libraries worldwide
Mathematics of Computing  Numerical Analysis
SchwarzChristoffel mapping by
Tobin A Driscoll(
Book
)
17 editions published in 2002 in English and held by 247 WorldCat member libraries worldwide
"This book provides a comprehensive look at the SchwarzChristoffel 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
17 editions published in 2002 in English and held by 247 WorldCat member libraries worldwide
"This book provides a comprehensive look at the SchwarzChristoffel 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
)
11 editions published between 2012 and 2013 in English and held by 187 WorldCat member libraries worldwide
11 editions published between 2012 and 2013 in English and held by 187 WorldCat member libraries worldwide
Numerical conformal mapping by
Lloyd N Trefethen(
Book
)
9 editions published between 1985 and 1986 in English and held by 104 WorldCat member libraries worldwide
9 editions published between 1985 and 1986 in English and held by 104 WorldCat member libraries worldwide
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 84 WorldCat member libraries worldwide
1 edition published in 1984 in English and held by 84 WorldCat member libraries worldwide
Surface tension in fluid mechanics(
Visual
)
14 editions published between 1964 and 2010 in English and held by 83 WorldCat member libraries worldwide
Presents a series of experiments to show that surfaces exert forces. Defines the fundamental boundary conditions 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
14 editions published between 1964 and 2010 in English and held by 83 WorldCat member libraries worldwide
Presents a series of experiments to show that surfaces exert forces. Defines the fundamental boundary conditions 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
A new direction in hydrodynamic stability beyond Eigenvalues by
Institute for Computer Applications in Science and Engineering(
Book
)
6 editions published in 1992 in English and held by 82 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 nonorthogonal eigenfunctions ... Hydrodynamic stability, Transition to turbulence
6 editions published in 1992 in English and held by 82 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 nonorthogonal eigenfunctions ... Hydrodynamic stability, Transition to turbulence
Fourier analysis of the SOR iteration by
Randall J LeVeque(
Book
)
6 editions published in 1986 in English and held by 78 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 spacetime 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
6 editions published in 1986 in English and held by 78 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 spacetime 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 freestreamline flow over a polygonal obstacle by
Alan R Elcrat(
Book
)
3 editions published in 1984 in English and held by 75 WorldCat member libraries worldwide
3 editions published in 1984 in English and held by 75 WorldCat member libraries worldwide
Wellposedness of oneway wave equations and absorbing boundary conditions by
Lloyd N Trefethen(
Book
)
4 editions published in 1985 in English and held by 73 WorldCat member libraries worldwide
4 editions published in 1985 in English and held by 73 WorldCat member libraries worldwide
Fundamentals of complex analysis for mathematics, science, and engineering by
E. B Saff(
Book
)
8 editions published between 1993 and 2008 in English and held by 17 WorldCat member libraries worldwide
This book provides a comprehensive introduction to complex variable theory and its applications to current engineering problems. It is designed to make the fundamentals of the subject more easily accessible to students who have little inclination to wade through the rigors of the axiomatic approach
8 editions published between 1993 and 2008 in English and held by 17 WorldCat member libraries worldwide
This book provides a comprehensive introduction to complex variable theory and its applications to current engineering problems. It is designed to make the fundamentals of the subject more easily accessible to students who have little inclination to wade through the rigors of the axiomatic approach
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
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 SchwarzChristoffel transformation by
Lloyd N Trefethen(
Book
)
5 editions published in 1979 in English and held by 7 WorldCat member libraries worldwide
A program is described which computes SchwartzChristoffel 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 GaussJacobi quadrature to evaluate the SchwarzChristoffel integral, making possible high accuracy at reasonable cost; and the elimination of constraints in the nonlinear system by a simple change of variables. SchwarzChristoffel transformations may be applied to solve the Laplace and Poisson equations and related problems in twodimensional 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 Ncubed, where N is the number of vertices of the polygon. A typical set of computations to 8place accuracy with N <or = 10 takes 1 to 10 seconds on an IBM 370/168. (Author)
5 editions published in 1979 in English and held by 7 WorldCat member libraries worldwide
A program is described which computes SchwartzChristoffel 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 GaussJacobi quadrature to evaluate the SchwarzChristoffel integral, making possible high accuracy at reasonable cost; and the elimination of constraints in the nonlinear system by a simple change of variables. SchwarzChristoffel transformations may be applied to solve the Laplace and Poisson equations and related problems in twodimensional 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 Ncubed, where N is the number of vertices of the polygon. A typical set of computations to 8place accuracy with N <or = 10 takes 1 to 10 seconds on an IBM 370/168. (Author)
Pseudospectra of the convectiondiffusion operator by Satish 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 convectiondiffusion 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 convectiondiffusion operators may be of limited value in some applications."
3 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Abstract: "The spectrum of the simplest ID convectiondiffusion 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 convectiondiffusion operators may be of limited value in some applications."
Special issue on numerical conformal mapping(
Book
)
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 5 WorldCat member libraries worldwide
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
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
GMRES/CR and Arnoldi/Lanczos as matrix approximation problems by
Anne Greenbaum(
Book
)
3 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1992 in English and held by 3 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
3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
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Related Identities
 Driscoll, Tobin A. (Tobin Allen) 1969 Author
 Bau, David
 Embree, Mark 1974
 Institute for Computer Applications in Science and Engineering
 Langley Research Center
 National Committee for Fluid Mechanics Films
 LeVeque, Randall J. 1955 Author
 Elcrat, Alan R. Author
 United States National Aeronautics and Space Administration
 Encyclopaedia Britannica Educational Corporation
Useful Links
Associated Subjects
Algebras, Linear Approximation theory Boundary value problems Canada Conformal mapping Difference equations Differential equations, Hyperbolic Differential equations, Linear Differential equations, Partial Differential equations, PartialNumerical solutionsData processing Differential operators Eigenvalues Finite differences Fluid mechanics Functions of complex variables Gaussian quadrature formulas Hydrodynamics Integral transforms Iterative methods (Mathematics) Mappings (Mathematics) Mathematical analysis Mathematical models Mathematicians Mathematics MATLAB Matrices Numerical analysis Numerical calculations Numerical integration SchwarzChristoffel transformation Scientists Spectral theory (Mathematics) Spectrum analysis Surface chemistry Surface tension Transformations (Mathematics) United States Wave equation
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 USamerikanischer 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
勞埃德·尼古拉斯·特雷費森
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