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Sobolev orthogonal polynomials with respect to measures supported on compact subsets of the complex plane are considered. For a wide class of such Sobolev orthogonal polynomials, it is proved that their zeros are contained in a compact subset of the complex plane and their asymptotic zero distribution is studied. We also find the nth root asymptotic… (More)

- G. LÓPEZ LAGOMASINO, L. WUNDERLICH, Richard S. Varga
- 2008

Many problems in science and engineering require the evaluation of functionals of the form Fu(A) = u T 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… (More)

We prove ratio asymptotic for sequences of multiple orthogonal poly-nomials with respect to a Nikishin system of measures N (σ1,. .. , σm) such that for each k, the support of σ k consists of an interval e ∆ k , on which σ ′ k > 0 almost everywhere, and a set without accumulation points in R \ e ∆ k .

We improve the class of indices for which normality takes place in a Nikishin system and apply this in Hermite-Padé approximation of such systems of functions.

Let be a finite positive Borel measure with compact support consisting of an interval [c, d] ⊂ R plus a set of isolated points in R\[c, d], such that > 0 almost everywhere on [c, d]. Let {w 2n }, n ∈ Z + , be a sequence of polynomials, deg w 2n 2n, with real coefficients whose zeros lie outside the smallest interval containing the support of. We prove ratio… (More)

We study the construction of a quadrature rule which allows the simultaneous integration of a given function with respect to different weights. This construction is built on the basis of simultaneous Padé approximation of a Nikishin system of functions. The properties of these approximants are used in the proof of convergence of the quadratures and… (More)

We study the zero location and asymptotic zero distribution of sequences of polynomials which satisfy an extremal condition with respect to a norm given on the space of all polynomials.

In this paper we investigate general properties of the coefficients in the recurrence relation satisfied by multiple orthogonal polynomials. The results include as particular cases Angelesco and Nikishin systems.

We consider the solutions of general three term recurrence relations whose coefficients are analytic functions in a prescribed region. We study the ratio asymptotic of such solutions under the assumption that the coefficients are asymptotically periodic and their strong asymptotic under more restrictive conditions.