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- Journal of Applied Mathematics and Physics (ZAMP) 0044-2275/84/005692413 $ 4.10/0 Vol. 35, September 1984 9 Birkh~iuser Verlag Basel, 1984
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- Advanced Problems: 6460-6462 L. Richard Duffy; L. E. Mattics; Randall J. LeVeque; Lloyd N. Trefethen
- Math.comput.sci. Online First c 2007 Birkhauser Verlag Basel/Switzerland
- Lecture 3. Norms The essential notions of size and distance in a vector space are captured by
- SIAM REVIEW Vol. 26, No. 3, July 1984
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- JOURNAL OF COMPUTATIONAL PHYSICS 49, 199-217 (1983) Group Velocity Interpretation
- Lecture 2. Orthogonal Vectors and Matrices Since the 1960s, many of the best algorithms of numerical linear algebra have
- Lecture 5. More on the SVD We continue our discussion of the singular value decomposition, emphasizing
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- Wave Packet Pseudomodes of Twisted Toeplitz Matrices
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- CHAPTER 6 TREFETHEN 1994 \Delta 219 Boundary Conditions
- CHAPTER 2 TREFETHEN 1994 \Delta 80 Fourier Analysis
- doi: 10.1098/rspa.2010.0506 published online 10 November 2010Proc. R. Soc. A
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- 1. Differentiation Matrices Our starting point is a basic question. Given a set of grid points fx j g and
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- Nick Trefethen, Oxford University Talbot quadratures
- Lewy-Hrmander nonexistence and pseudospectra
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- JOURNAL OF APPROXIMATION THEORY 39.275-288 (1983) Nonuniqueness of Best Rational Chebyshev
- Nick Trefethen, 7 November 1997 TRANSITION TO TURBULENCE IN CHANNELS AND PIPES
- Low-dimensional models of subcritical transition to turbulence Jeffrey S. Baggetta)
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- Wide-angleone-way wave equations LaurenceHalpern
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- MultiMATLAB: MATLAB on Multiple Processors
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- Lecture 1. MatrixVector Multiplication You already know the formula for matrixvector multiplication. Nevertheless,
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- Continuous analogues of QR, SVD, and LU
- Wave packet pseudomodes of variable coefficient differential operators
- CHAPTER 7 TREFETHEN 1994 232 Fourier spectral methods
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- CHAPTER 8 TREFETHEN 1994 \Delta 260 Chebyshev spectral methods
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- A robust implementation of the Caratheodory-Fejer Joris Van Deun and Lloyd N. Trefethen
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- Electronic Transactions on Numerical Analysis. Volume 29, pp. 1-18, 2007.
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- Computed eigenmodes of planar regions Lloyd N. Trefethen and Timo Betcke
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- IMA Journal of Numerical Analysis (2002) 22, 501519 Pseudospectra of rectangular matrices
- Computational Methods and Function Theory Volume 1 (2001), No. 1, 259273
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- LARGE-SCALE COMPUTATION OF PSEUDOSPECTRA USING ARPACK AND EIGS
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- arXiv:physics/0007092v1[physics.flu-dyn]28Jul2000 Threshold amplitudes for transition to turbulence in a pipe
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- Const~Approx. (1990) 6:195-223 CONSTRUCTIVE
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- IMA Journal of Numerical Analysis (1988) 8, 273-279 Fourier Analysis of the SOR Iteration
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- 21. Beam equation When you ping a ruler projecting a length L over the edge of a table, the frequency is inversely
- 24. KdV equation The Korteweg{de Vries equation has a colourful history, which began in 1832 with John Scott
- 3.Constantcoe cientlinearequations The most basic of all problems involving partial di erential equations are linear PDEs with constant
- 9. Capillary surface equation It would be di cult to pass a day on this planet without encountering capillary phenomena. Cap-
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- 29. Compacton equations The KdV equation ut = (u2)x + uxxx (! ref ) mixes nonlinear convection with linear dispersion.
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- 34.Advection{di usion equations In uid mechanics, meteorology, semiconductor device modelling, ecology, oil reservoir simulation,
- Hydrodynamic Stability Without Eigenvalues Author(s): Lloyd N. Trefethen, Anne E. Trefethen, Satish C. Reddy, Tobin A. Driscoll
- 31. Lewy equation 2i(x + iy)ut = ux + iuy (1)
- 8. Minimal surface equation Fig. 1: helicoid
- 3. Heat equation The heat equation is the prototypical parabolic PDE
- 19. One-way wave equations The second-order wave equation (! ref ) is isotropic: invariant with respect to rotation in space. In
- 45. Cahn{Hilliard equation The Allen{Cahn equation ut = u u3 + u describes regions with u 1 and u 1 that grow
- 15. Wave equation in 1D In one dimension the wave equation (! ref ) takes the form
- 46. Perona{Malik equation The heat equation ut = u is the canonical smoothing process, di using data at a constant rate
- 3. Backward heat equation Some physical processes are reversible in the sense that changing the direction of time makes no
- 37. Fisher-KPP equation A reaction{di usion equation looks like the heat equation (! ref ) with a function f (u) added on,
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- 31. Blow-up equation with eu nonlinearity The equation ut = r2u + eu
- 23. Gray{Scott equations Patterns are everywhere in nature. Examples include spots on butter ies, stripes on zebras, tri-
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- 29. Boussinesq Equation Russell's discovery of solitary waves in the 1840s (! ref ) raised a challenge: to devise a mathemat-
- 59. Klein{Gordon equation The Klein{Gordon equation dates to the legendary early period of development of quantum me-
- 58. Equations of uid mechanics It is probably fair to say that half the subject of PDEs has its roots in uid mechanics. Almost every
- 7. Laplace equation The Laplace equation is so important that functions that satisfy it have a special name: they are
- 29. Blow-up equation with up nonlinearity There are many mathematical models of physical problems which result in solutions that develop
- 21. Time-dependent Schrodinger equation The Schrodinger equation, the basis of quantum mechanics, was discovered by Erwin Schrodinger
- 38. Allen{Cahn orbistable equation The Fisher equation (!ref), with reaction term f(u) = u(1 u), admits a stable equilibrium state
- 51. Inviscid Burgers equation A PDE of the form ut + (f(u))x = 0 is called a conservation law, with u representing the density
- 15. Wave equation One of the \holy Trinity" of partial di erential equations is the second{order wave equation, the
- 35. Porous medium equation The porous medium equation is like the heat equation (! ref ), except that the linear di usion term
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- 17. Helmholtz Equation The Helmholtz equation, or reduced wave equation, has the form
- 26. Sine{Gordon equation In view of the remarkable properties of the KdV equation (! ref ), it is natural to ask whether other
- 42. Eigenfunctions of the Laplace equation Earlier we alluded to the eigenfunctions of the Laplace operator in a box or a ball (! ref ). There
- 47. Kuramoto{Sivashinsky equation The Kuramoto{Sivashinsky equation in one space dimension is given in two standard forms. The
- ROBUST PADE APPROXIMATION VIA SVD PEDRO GONNET, STEFAN GUTTEL, AND LLOYD N. TREFETHEN
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- Publications by Lloyd N. Trefethen I.1. Numerical Conformal Mapping, editor, 269 pages. Elsevier, 1986.
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- From SIAM News, Volume 45, Number 1, January/February 2012 Iain Duff, one of the pillars of Western applied mathematical civilization, is on my mind this