Maria Antónia Forjaz

On an enumerative algorithm for solving eigenvalue complementarity problems

In this paper, we discuss the solution of linear and quadratic eigenvalue complementarity problems (EiCPs) using an enumerative algorithm of the type introduced by Júdice etxa0al. (Optim. Methods Softw. 24:549–586, 2009). Procedures for computing the interval that contains all the eigenvalues of the linear EiCP are first presented. A nonlinear programming (NLP) model for the quadratic EiCP is formulated next, and a necessary and sufficient condition for a stationary point of the NLP to be a solution of the quadratic EiCP is established. An extension of the enumerative algorithm for the quadratic EiCP is also developed, which solves this problem by computing a global minimum for the NLP formulation. Some computational experience is presented to highlight the efficiency and efficacy of the proposed enumerative algorithm for solving linear and quadratic EiCPs.

Visco-elastic systems as a quadratic eigenvalue problem

The author Maria Antonia Forjaz acknowledges the funding supported by Portuguese Funds through FCT - ’Fundacao para a Ciencia e a Tecnologia’, UID/MAT/00013/2013. nThe author Jorge Pamplona is co-funded by the European Union through the European Regional Development Fund, based on COMPETE 2020 (Programa Operacional da Competitividade e Internacionalizacao), project ICT (UID/GEO/04683/2013) with reference POCI-01-0145-FEDER-007690 and national funds provided by Fundacao para a Ciencia e Tecnologia. nThe authors Antonio Mario Almeida and T. de Lacerda–Aroso acknowledge the support of the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UID/FIS/04650/2013.

Parallelization of an Algorithm for Computing the Eigenelements of an Astrophysics Model

The integral formulation of the transfer problem that represents the restriction of a strongly coupled system of nonlinear equations dealing with radiative transfer in stellar atmospheres is our test problem. Computational approaches in open source packages that consider parallel implementations, to solve the spectral problem is considered.

An Efficient Parallel Algorithm for the Symmetric Tridiagonal Eigenvalue Problem

An efficient parallel algorithm, which we dubbed farmzeroinNR, for the eigenvalue problem of a symmetric tridiagonal matrix has been implemented in a distributed memory multiprocessor with 112 nodes [1]. The basis of our parallel implementation is an improved version of the zeroinNR method [2]. It is consistently faster than simple bisection and produces more accurate eigenvalues than the QR method. As it happens with bisection, zeroinNR exhibits great flexibility and allows the computation of a subset of the spectrum with some prescribed accuracy. Results were carried out with matrices of different types and sizes up to 104 and show that our algorithm is efficient and scalable.