Computational linear algebra aspects
This chapter is devoted to computational aspects of the practical preparation of all ingredients of admissible matrix function sequences and the associate projectors. Eventually one has to carry out matrix factorizations, rank calculations, and generalized inverses. The characteristic values as well as the tractability index arise as byproducts of certain matrix factorizations. We provide several versions to accomplish the basic step of the matrix function sequence from one level to the next. These tools apply to general rectangular DAEs. Thereby, from the numerical viewpoint, the so-called widely orthogonal projector functions prove to be favorable. Further, a special more involved algorithm is developed for regular DAEs. The provided algorithms can be applied to check regularity and to monitor the characteristic values and the index.
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