N−variable rational approximants and method of moments
نویسندگان
چکیده
منابع مشابه
Effective Computation of Rational Approximants and Interpolants
This paper considers the problem of effective algorithms for some problems having structured coefficient matrices. Examples of such problems include rational approximation and rational interpolation. The corresponding coefficient matrices include Hankel, Toeplitz and Vandermonde-like matrices. Effective implies that the algorithms studied are suitable for implementation in either a numeric envi...
متن کاملOrthorhombic rational approximants for decagonal quasicrystals
An important exercise in the study of rational approximants is to derive their metric, especially in relation to the corresponding quasicrystal or the underlying clusters. Kuo’s model has been the widely accepted model to calculate the metric of the decagonal approximants. Using an alternate model, the metric of the approximants and other complex structures with the icosahedral cluster are expl...
متن کاملMatrices, Moments, and Rational Quadrature
Abstract. Many problems in science and engineering require the evaluation of functionals of the form Fu(A) = uT f(A)u, where A is a large symmetric matrix, u a vector, and f a nonlinear function. A popular and fairly inexpensive approach to determining upper and lower bounds for such functionals is based on first carrying out a few steps of the Lanczos procedure applied to A with initial vector...
متن کاملConvergence in Capacity of Rational Approximants of Meromorphic Functions
Let f be meromorphic on the compact set E ⊂ C with maximal Green domain of meromorphy Eρ(f), ρ(f) < ∞. We investigate rational approximants with numerator degree 6 n and denominator degree 6 mn for f . We show that the geometric convergence rate on E implies convergence in capacity outside E if mn = o(n) as n → ∞. Further, we show that the condition is sharp and that the convergence in capacity...
متن کاملRAY SEQUENCES OF BEST RATIONAL APPROXIMANTS FOR Ixla
The convergence behavior of best unifonn rational approximations r;'n with numerator degree m and denominator degree n to the function Ixla, a > 0, on [-I, I] is investigated. It is assumed that the indices (m, n) progress along a ray sequence in the lower triangle of the Walsh table, i.e. the sequence of indices {(m, n)} satisfies m --c E [1,00) asm+If-OO. If In addition to the convergence beh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1975
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.522617