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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 .

- Alexander I. Aptekarev, Valeriy A. Kalyagin, Guillermo López Lagomasino, I. A. Rocha
- Journal of Approximation Theory
- 2006

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.

- Guillermo López Lagomasino, I. Pérez Izquierdo, H. Pijeira Cabrera
- Journal of Approximation Theory
- 2005

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.

- Amílcar José Pinto Lopes Branquinho, Jorge Bustamante, Ana Pilar Foulquié Moreno, Guillermo López Lagomasino
- Journal of Approximation Theory
- 2003

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.

- Ulises Fidalgo Prieto, J. Illán, Guillermo López Lagomasino
- Journal of Approximation Theory
- 2004

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)

- Dolores Barrios Rolanía, Bernardo de la Calle Ysern, Guillermo López Lagomasino
- Journal of Approximation Theory
- 2006

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)

- Ulises Fidalgo Prieto, Jesús R. Illán González, Guillermo López Lagomasino
- Numerische Mathematik
- 2007

- Dolores Barrios Rolanía, Guillermo López Lagomasino
- Adv. Comput. Math.
- 2007

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.