This paper presents detailed aspects regarding the implementation of Finite Element Method (FEM) to solve a Poisson’s equation with homogeneous boundary conditions. The aim this is clarify details implementation, such as construction algorithms, numerical experiments, and their results. For purpose, continuous problem described, classical FEM approach used it. In addition, multilevel technique implemented for an efficient resolution corresponding linear system, describing including some...

We study some aspects of the invariant pair problem for matrix polynomials, as introduced by Betcke and Kressner Beyn Thuemmler. Invariant pairs extend notion eigenvalue-eigenvector pairs, providing a counterpart subspaces nonlinear case. compute formulations condition numbers backward errors solvents. then adapt Sakurai-Sugiura moment method to computation including classes problems that have multiple eigenvalues. Numerical refinement via variants Newton's is also studied. Furthermore, we...

We consider the matrix polynomial [EQUATION], with given coefficients [EQUATION]. A [EQUATION] is called a solvent if P(S) = 0. explore some approaches to symbolic and numeric computation of solvents. In particular, we compute formulas for condition number backward error problem which rely on contour integral based representation P(S). Finally, describe possible approach computing exact solvents symbolically.

We study the problem of approximating zeros an univariate polynomial (up to machine precision). Some popular iterative root-finding methods construct companion matrices (Frobenius, Lagrange) associated with given and use eigensolvers find eigenvalues such matrices. Our goal is this technique, exploiting structure (e.g., diagonal plus rank one) obtain a decrease computational cost memory requirements.

En este artículo estudiamos fundamentalmente las denominadas secuencias tipo Turyn y algunos algoritmos heurísticos para generarlas. La importancia de estas estriba, al menos, en el hecho que pueden ser empleadas la construcción algunas matrices Hadamard órdenes 4(3m - 1), donde m es largo secuencia a través del uso teorema Goethals-Seidal. Simplificamos demostración (ver Teorema 3). Además, hallamos resultados teóricos interesantes 5). Finalmente, desarrollamos varios eficientes,...

Time series anomaly detection is an important process for system monitoring and model switching, among other applications in cyber-physical systems. In this document, we present a fast subspace method time detection, with relatively low computational cost, that has been designed real sensor signals corresponding to dynamical We also some general results the theoretical foundations of our method, together prototypical algorithm detection. Some numerical examples are presented, tools based on...

We propose a novel method for building fuzzy clusters of large data sets, using smoothing numerical approach. The usual sum-of-squares criterion is relaxed so the search good partitions made on continuous space, rather than combinatorial space as in classical methods \cite{Hartigan}. allows conversion from strongly non-differentiable problem into differentiable subproblems optimization without constraints low dimension, by function infinite class. For implementation algorithm we used...

Time series anomaly detection is an important process for system monitoring and model switching, among other applications in cyber-physical systems. In this document we present a fast subspace method time detection, with relatively low computational cost, that has been designed real sensor signals corresponding to dynamical We also some general results the theoretical foundations of our method, together prototypical algorithm detection. Some numerical examples are presented, tools based on...