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We present variants of the block-GMRES($m$) algorithms due to Vital and the block-LGMRES($m$,$k$) by Baker, Dennis and Jessup, obtained with replacing the standard QR factorization by a rank-revealing QR factorization in the Arnoldi process. The resulting algorithm allows for dynamic block deflation whenever there is a linear dependency between the Krylov vectors or the convergence of a right-hand-side occurs. $\textsc{Fortran 90}$implementations of the algorithms were tested on a number of test matrices and the results show that in some cases a substantial reduction of the execution time is obtained. Also a parallel implementation of our variant of the block-GMRES($m$) algorithm, using $\textsc{Fortran 90}$and $\textsc{MPI}$was tested on $\textsc{SunFire 15K}$parallel computer, showing good parallel efficiency.

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Este trabalho apresenta um modelador 3D utilizado como ferramenta de ensino-aprendizagem de geometria descritiva através do paradigma do design-based learning. O HyperCAL 3D foi desenvolvido para que os alunos possam representar em 3D os projetos elaborados a partir dos conceitos de geometria descritiva e, assim, estabelecer relações entre as representações convencionais e a geometria dos objetos em três dimensões. O programa foi implementado em linguagem Delphi e utiliza a realidade virtual, através da linguagem VRML, para visualização dos objetos gerados. A utilização desta ferramenta inovadora tem permitido um salto de qualidade na aprendizagem da geometria descritiva como pode ser visto nos exemplos de projetos desenvolvidos pelos alunos.

This work reports the experience in the implementation of a new paradigm in teaching of descriptive geometry: the Design-based learning. This paradigm changing is the result of a new approach centered on the student, seeking to develop its creativity and its own problem solving capacity based on the descriptive geometry concepts. In this sense, all the concepts and projects developed implicate working with solids. Therefore, it implies in the increasing of the concrete experience, reducing the usual abstraction level needed to learn the fundamental concepts. The proposed methodology was first implemented in some sample classes of Engineering and Design courses of the Federal University of Rio Grande do Sul (UFRGS) with great success.

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