Guillermo López Lagomasino

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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 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)
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 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.