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Inverse polynomial expansions of Laurent series
Springer Science and Business Media LLC - Tập 4 Số 1 - Trang 379-389 - 1988
Arnold Knopfmacher, John Knopfmacher
Wall Polynomials on the Real Line: A Classical Approach to OPRL Khrushchev’s Formula
Springer Science and Business Media LLC - - 2023
Maŕıa José Cantero, Leandro del Moral Ituarte, L. Velázquez
AbstractThe standard proof of Khrushchev’s formula for orthogonal polynomials on the unit circle given in Khrushchev (J Approx Theory 108:161–248, 2001, J Approx Theory 116:268–342, 2002) combines ideas from continued fractions and complex analysis, depending heavily on the theory of Wall polynomials. Using operator theoretic tools instead, Khrushchev’s formula has been recently extended to the se... hiện toàn bộ
On the Markov Inequality in the $$L_2$$ L 2 -Norm with the Gegenbauer Weight
Springer Science and Business Media LLC - Tập 49 Số 1 - Trang 1-27 - 2019
Geno Nikolov, Alexei Shadrin
The left-definite Legendre type boundary problem
Springer Science and Business Media LLC - Tập 7 - Trang 485-500 - 1991
W. N. Everitt, L. L. Littlejohn, S. C. Williams
The left-definite Legendre type boundary problem concerns the study of a fourth-order singular differential expressionM k [−] in a weighted Sobolev spaceH generated by a Dirichlet inner product. The fourth-order differential equation $$M_k [y] = \lambda y$$ has orthogonal polynomial eigenfunctions, called the Legendre type polynomials, associated with the eigenvalues $$\lambda _n = n(n + 1)(n^2 + ... hiện toàn bộ
Simple Cubature Formulas with High Polynomial Exactness
Springer Science and Business Media LLC - Tập 15 - Trang 499-522 - 1999
Erich Novak, Klaus Ritter
We study cubature formulas for d -dimensional integrals with arbitrary weight function of tensor product form. We present a construction that yields a high polynomial exactness: for fixed degree, the number of knots depends on the dimension in an order-optimal way. The cubature formulas are universal: the order of convergence is almost optimal for two different scales of function spaces. The const... hiện toàn bộ
The Diagonal of the Padé Table and the Approximation of the Weyl Function of Second-Order Difference Operators
Springer Science and Business Media LLC - - 1997
Bernhard Beckermann, V. Kaliaguine
Splines on Triangulations with Hanging Vertices
Springer Science and Business Media LLC - Tập 36 - Trang 487-511 - 2012
Larry L. Schumaker, Lujun Wang
Polynomial spline spaces defined on triangulations with hanging vertices are studied. In addition to dimension formulae, explicit basis functions are constructed, and their supports and stability are discussed. The approximation power of the spaces is also treated.
Quadratic Convergence of Newton's Method for Convex Interpolation and Smoothing
Springer Science and Business Media LLC - Tập 19 - Trang 123-143 - 2003
Dontchev, Qi
Abstract. In this paper, we prove that Newton's method for convex best interpolation is locally quadratically convergent, giving an answer to a question of Irvine, Marin, and Smith [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. A damped Newton-type method is presented which has global quadratic convergence. Analogous results are obtained for the convex smoot... hiện toàn bộ
Hermite Interpolation of Data Sets by Minimal Spline Spaces
Springer Science and Business Media LLC - Tập 23 - Trang 211-227 - 2005
Manfred Sommer
Hermite interpolation of 2n + k data by spline spaces of order k with n variable knots counting multiplicities is studied. A characterization of the minimal spline spaces which admit a solution of the interpolation problem is obtained. A sufficient condition on uniqueness of interpolating spline functions is given.
Strong Asymptotics for Bergman Polynomials over Domains with Corners and Applications
Springer Science and Business Media LLC - Tập 38 - Trang 59-100 - 2012
Nikos Stylianopoulos
Let G be a bounded simply-connected domain in the complex plane ℂ, whose boundary Γ:=∂G is a Jordan curve, and let $\{p_{n}\}_{n=0}^{\infty}$ denote the sequence of Bergman polynomials of G. This is defined as the unique sequence $$p_n(z) = \lambda_n z^n+\cdots, \quad \lambda_n>0,\ n=0,1,2,\ldots, $$ of polynomials that are orthonormal with respect to the inner product $$\langle f,g\rangle := \int... hiện toàn bộ
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