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Regions of stability, equivalence theorems and the Courant-Friedrichs-Lewy condition
Springer Science and Business Media LLC - Tập 49 - Trang 319-329 - 1986
The celebrated CFL condition for discretizations of hyperbolic PDEs is shown to be equivalent to some results of Jeltsch and Nevanlinna concerning regions of stability ofk-step,m-stage linear methods for the integration of ODEs. We characterize the methods for the numerical integration of the model equation,u
t=u
x which are weakly stable when the mesh-ratio takes the maximum value allowed by the ...... hiện toàn bộ
On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
Springer Science and Business Media LLC - Tập 2 - Trang 84-90 - 1960
Interpolation error estimates in W 1,p for degenerate Q 1 isoparametric elements
Springer Science and Business Media LLC - Tập 104 - Trang 129-150 - 2006
Optimal order error estimates in H
1, for the Q
1 isoparametric interpolation were obtained in Acosta and Durán (SIAM J Numer Anal37, 18–36, 1999) for a very general class of degenerate convex quadrilateral elements. In this work we show that the same conlusions are valid in W
1,p
for 1≤ p < 3 and we g...... hiện toàn bộ
C-Polynomials for rational approximation to the exponential function
Springer Science and Business Media LLC - Tập 25 Số 1 - Trang 39-56 - 1975
A unique correspondence between (m, n) rational approximations to exp (q) of order at leastm and a polynomial of degreen, theC-polynomial, is obtained. This polynomial is then used to find an effective result regarding theA-acceptability of these approximations.
Sparse harmonic transforms II: best s-term approximation guarantees for bounded orthonormal product bases in sublinear-time
Springer Science and Business Media LLC - Tập 148 - Trang 293-362 - 2021
In this paper we develop a sublinear-time compressive sensing algorithm for approximating functions of many variables which are compressible in a given Bounded Orthonormal Product Basis (BOPB). The resulting algorithm is shown to both have an associated best s-term recovery guarantee in the given BOPB, and also to work well numerically for solving sparse approximation problems involving functions ...... hiện toàn bộ
Etudes sur les ε- et ρ-algorithmes
Springer Science and Business Media LLC - Tập 17 - Trang 153-162 - 1971
Some methods of accelerating the convergence of sequences are studied herein. It is shown that, in some special cases, the convergence of the ε-algorithm of Wynn is assured. A modification of this algorithm is then proposed which may still accelerate the convergence toward the limit. Finally, a new ϱ-algorithm is given in which the dependence with respect to a parameter is explicitely introduced.
Boundary element methods for Maxwell's equations on non-smooth domains
Springer Science and Business Media LLC - Tập 92 - Trang 679-710 - 2002
Variational boundary integral equations for Maxwell's equations on Lipschitz surfaces in
${\mathbb R}^3$
are derived and their well-posedness in the appropriate trace spaces is established. An equivalent, stable mixed reformulation of the system of integral equations is obtained which admits discretization by Galerkin boundary elements based on standard spaces....... hiện toàn bộ
A finite element method for the numerical solution of convection-dominated anisotropic diffusion equations
Springer Science and Business Media LLC - Tập 85 - Trang 175-195 - 2000
The proposed method is based on an additive decomposition of the differential operator and the subsequent fitted discretization of the resulting components. For standard situations, the derived stability and error estimates in the energy norm qualitatively coincide with well-known estimates. In the case of small diffusion, a uniform error estimate with reduced order is obtained.
Power series equivalent to rational functions: A shifting-origin kronecker type theorem, and normality of Padé tables
Springer Science and Business Media LLC - Tập 54 - Trang 33-39 - 1988
Letf(z) be a function analytic in a neighbourhood of zero. For each pair of non-negative integers (m, n), form then byn Toeplitz determinantD(m/n) whose entries are the Maclaurin series coefficients off, namely,
$$D(m/n): = det[f^{(m + j - k)} (0)/(m + j - k)!]_{j,k = 1'}^n $$
where we definef
...... hiện toàn bộ
A class of simple exponential B-splines and their application to numerical solution to singular perturbation problems
Springer Science and Business Media LLC - - 1989
We shall consider an application of simple exponential splines to the numerical solution of singular perturbation problem. The computational effort involved in our collocation method is less than that required for the other methods of exponential type.
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