Mixed precision bisection

We discuss the implementation of the bisection algorithm for the computation of the eigenvalues of symmetric tridiagonal matrices in a context of mixed precision arithmetic. This approach is motivated by the emergence of processors which carry out floating-point operations much faster in single precision than they do in double precision. Perturbation theory results are used to decide when to switch from single to double precision. Numerical examples are presente

Matrix arithmetic-geometric mean and the computation of the algorithm

We investigate the stability of the matrix arithmetic-geometric mean (AGM) iteration. We show that the classical formulation of this iteration may be not stable (a necessary and su cient condition for its stability is given) and investigate the numerical properties of alternative formulations. It turns out that the so-called Legendre form is the right choice for matrices. Due to its fast convergence and good numerical properties, our AGM formulation has the potential to play an important role in the computation of matrix functions. In fact, we developed an algorithm, whose main block is an optimized AGM scheme, for the computation of the logarithm of a matrix, which is shown to be competitive, in terms of accuracy, with the state-of-the-art methods. Methods that do not require an initial reduction to the Schur form are potentially more e cient on parallel computers. For this reason, our current implementation does not include such reduction and operates with full matrices till the end. As compared to the state-of-the-art reduction free algorithm, our method relies more heavily on matrix multiplications, which are highly suited to modern architectures, and requires a smaller number of multiple right-hand-side linear systems, making it competitive also in terms of computational e ciency. Our claims are supported with analysis and also with numerical results produced with a MATLAB code

Very high-order finite volume method for one-dimensional convection diffusion problems

We propose a new finite volume method to provide very high-order accuracy for the convection diffusion problem. The main tool is a polynomial reconstruction based on the mean-value to provide the best order. We give simple numerical examples that illustrate the effectiveness of the method in attaining the expected order of convergence.This research was financed by FEDER Funds through Programa Operacional Factores de Competitividade — COMPETE and by Portuguese Funds through FCT — Fundação para a Ciência e a Tecnologia, within the Project PEst- C/MAT/UI0013/2011

A Flexible Curriculum for Computer Science Undergraduate Major

This paper describes an innovative approach to establish a CS curriculum, aiming flexibility and minimization of the time spent in the classrooms. This approach has been developed at the Paulista State University - Unesp - at S ao Jos e do Rio Preto, and is producing very interesting results. The load reduction is achieved through a series of fundamental core and breadth courses that precede depth courses in specific areas. The flexibility comes as a side effect of the depth courses, which can be adapted without any changes in the core courses. In the following pages we fully describe our motivations, actions and results