Algorithms for Structured Linear Systems Solving and Their Implementation

There exists a vast literature dedicated to algorithms for structured matrices, but relatively few descriptions of actual implementations and their practical performance in symbolic computation. In this paper, we consider the problem of solving Cauchy-like systems, and its application to mosaic Toeplitz systems, in two contexts: first in the unit cost model (which is a good model for computations over finite fields), then over Q. We introduce new variants of previous algorithms and describe an implementation of these techniques and its practical behavior. We pay a special attention to particular cases such as the computation of algebraic approximants.

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