共查询到20条相似文献,搜索用时 15 毫秒
1.
《Applied Numerical Mathematics》1987,3(6):529-538
A method for the numerical inversion of the Laplace transform of a functions f is to approximate it by rational functions fm(z), and then to use the inverse transforms Fm(t) of fm(z) as approximation of the inverse transform F(t) of f(z).As in Tricomi's method we define fm(z) as a partial sum of a series expansion, which is also a Padé-type approximant to f with one pole. Then Fm(t) is the partial sum of the expansion of F(t) in terms of Laguerre polynomials.We prove mean square and uniform convergence results. The study for the choice of the pole of fm is used to define a best Padé-type approximant with one pole. It permits the use of the method of inversion by Laguerre polynomials, with good numerical results for functions having essential singularities. 相似文献
2.
C. Brezinski 《Numerical Algorithms》1999,21(1-4):97-107
It is shown that Krylov subspace methods for solving systems of linear equations can be based on formal biorthogonal polynomials
and on Padé-type and Padé approximants. New algorithms for their implementation are derived.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
P. Sablonnière 《Numerical Algorithms》2014,66(2):339-347
We prove that sequences generated by the generalized Euler’s transform can be considered as Padé-type approximants obtained by Hermite interpolation of the generating function \(u \rightarrow (1+xu)^{-1}\) at the endpoints of the interval \([0,1]\) . A first natural extension is then proposed by considering Hermite interpolation at multiple points of larger intervals. 相似文献
4.
5.
6.
We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416. 相似文献
7.
8.
We prove that certain two-point Padé approximants occupying the diagonal of the Padé table form monotone sequences of lower and upper bounds uniformly converging to a Stieltjes function. The results can be applied to the theory of inhomogeneous media for the calculation of the bounds on the effective transport coefficients of heterogeneous materials. 相似文献
9.
The connection between orthogonal polynomials, Padé approximants and Gaussian quadrature is well known and will be repeated
in section 1. In the past, several generalizations to the multivariate case have been suggested for all three concepts [4,6,9,...],
however without reestablishing a fundamental and clear link. In sections 2 and 3 we will elaborate definitions for multivariate
Padé and Padé-type approximation, multivariate polynomial orthogonality and multivariate Gaussian integration in order to
bridge the gap between these concepts. We will show that the new m-point Gaussian cubature rules allow the exact integration of homogeneous polynomials of degree 2m−1, in any number of variables. A numerical application of the new integration rules can be found in sections 4 and 5.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
10.
Wynn used generalized inverses to interpret continued fractions containing vector-valued elements. This approach led to the introduction of generalized inverse, vector-valued Padé approximants (GIPAs). All possible cases of degeneracy of GIPAs are analysed in this paper. We derive linear equations for the coefficients of the denominator polynomial of a GIPA. The solution of these equations allows construction of a GIPA in all cases where such a GIPA exists. We show that the block structure of the table of GIPAs is precisely analogous to that of the Padé table.Communicated by Edward B. Saff. 相似文献
11.
This paper is concerned with double sequencesC={C
n}
n
=–/
of Hermitian matrices with complex entriesC
n
M
s×s
) and formal Laurent seriesL
0(z)=–
k=1
C
–k
z
k
andL
(z)=
k=0
C
k
z
–k
. Making use of a Favard-type theorem for certain sequences of matrix Laurent polynomials which was obtained previously in [1] we can establish the relation between the matrix counterpart of the so-calledT-fractions and matrix orthogonal Laurent polynomials. The connection with two-point Padé approximants to the pair (L
0,L
) is also exhibited proving that such approximants are Hermitian too. Finally, error formulas are also given. 相似文献
12.
《Journal of Computational and Applied Mathematics》2002,145(1):99-112
A Stieltjes function is expanded in mixed T- and S-continued fraction. The relations between approximants of this continued fraction and two-point Padé approximants are established. The method used by Gilewicz and Magnus (J. Comput. Appl. Math. 49 (1993) 79; Integral Transforms Special Functions 1 (1993) 9) has been adapted to obtain the exact relations between the errors of the contiguous two-point Padé approximants in the whole cut complex plane. 相似文献
13.
Dušan Lj. Djukić Aleksandar V. Pejčev Miodrag M. Spalević 《Numerical Algorithms》2018,77(4):1003-1028
We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szeg? weight functions consisting of any one of the four Chebyshev weights divided by the polynomial \(\rho (t)=1-\frac {4\gamma }{(1+\gamma )^{2}}\,t^{2},\quad t\in (-1,1),\ -1<\gamma \le 0\). For analytic functions, the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points ? 1 and sum of semi-axes ρ > 1, for the given quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed by S. Notaris (Numer. Math. 103, 99–127, 2006). 相似文献
14.
Sotirios E. Notaris 《Numerische Mathematik》2006,103(1):99-127
We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szegö weight functions consisting of any one of the four Chebyshev weights divided by the polynomial On certain spaces of analytic functions, the error term of these formulae is a continuous linear functional. We compute explicitly the norm of the error functional. 相似文献
15.
It is possible to formulate the polynomial Szemerédi theorem as follows: Let q
i
(x) ∈ Q[x] with q
i
(Z) ⊂ Z, 1 ≤ i ≤ k. If E ⊂ N has positive upper density, then there are a, n ∈ N such that
(n) - q_1 (0),...,a + q_k (n) - q_k (0) E. |
#xA;
\{ a,a + q_1 (n) - q_1 (0),...,a + q_k (n) - q_k (0)\} \subset E.
相似文献
16.
We study some discrete isoperimetric and Poincaré-type inequalities for product probability measures μ
n
on the discrete cube {0, 1}
n
and on the lattice Z
n
. In particular we prove sharp lower estimates for the product measures of boundaries of arbitrary sets in the discrete cube.
More generally, we characterize those probability distributions μ on Z which satisfy these inequalities on Z
n
. The class of these distributions can be described by a certain class of monotone transforms of the two-sided exponential
measure. A similar characterization of distributions on R which satisfy Poincaré inequalities on the class of convex functions is proved in terms of variances of suprema of linear
processes.
Received: 30 April 1997 / Revised version: 5 June 1998 相似文献
17.
18.
Hans Wallin 《Applicable analysis》2013,92(3):235-251
Let f be a power series ∑aizi with complex coefficients. The (n. n) Pade approximant to f is a rational function P/Q where P and Q are polynomials, Q(z) ? 0, of degree ≦ n such that f(z)Q(z)-P(z) = Az2n+1 + higher degree terms. It is proved that if the coefficients ai satisfy a certain growth condition, then a corresponding subsequence of the sequence of (n, n) Pade approximants converges to f in the region where the power series f converges, except on an exceptional set E having a certain Hausdorff measure 0. It is also proved that the result is best possible in the sense that we may have divergence on E. In particular,there exists an entire function f such that the sequence of (ny n) Pade approximants diverges everywhere (except at 0) 相似文献
19.
I. I. Sharapudinov 《Mathematical Notes》1997,62(4):501-512
Suppose that 0<δ≤1,N=1/δ, and α, ga≥0, is an integer. For the classical Meixner polynomials
orthonormal on the gird {0, δ, 2δ, ...} with weight ρ(x)=(1-e
−δ)αг(Nx+α+ 1)/г(Nx+1), the following asymptotic formula is obtained:
. The remainderv
n,N
α
(z) forn≤λN satisfies the estimate
20.
We investigate the convergence of sequences of Padé approximants for the partial theta function $$h_q (z): = \sum\limits_{j = 0}^\infty { q^{j(j - 1)/2_{Z^j } } } , q = e^{i\theta } , \theta \in [0,2\pi ).$$ Whenθ/(2π) is irrational, this function has the unit circle as its natural boundary. We determine subrogions of ¦z¦ < 1 in which sequences of Padé approximants converge uniformly, and subrogions in which they converge in capacity, but not uniformly. In particular, we show that only a proper subsequence of the diagonal sequence {[n/n]} n=1 ∞ converges locally uniformly in all of ¦z¦< l; in contrast, no subsequence of any Padé row {[m/n]} m=1 ∞ (withn ≥ 2 fixed) can converge locally uniformly in all of ¦z¦ < 1. Further, we obtain the zero and pole distributions of sequences of Padé approximants by analyzing the zero distribution of the Rogers-Szegö polynomials $$G_n (z): = \sum\limits_{j = 0}^n {\left[ {\begin{array}{*{20}c} n \\ j \\ \end{array} } \right]} z^j , n = 0,1,2,....$$ 相似文献
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