Straight-line computation of the polynomial matrix inverse

Abstract : We present an inversion algorithm for nonsingular n x n matrices whose entries are degree d polynomials over a field. The algorithm is deterministic and requires O~(n^3d) field operations for a generic input. The ``soft Oh'' notation O~ indicates some missing log(nd) factors. The polynomial matrix inverse can thus be computed by a straight-line program whose size is - asymptotically and up to logarithmic factors - the size of its output.
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Claude-Pierre Jeannerod, Gilles Villard. Straight-line computation of the polynomial matrix inverse. [Research Report] LIP RR-2002-47, Laboratoire de l'informatique du parallélisme. 2002, 2+10p. ⟨hal-02101970⟩

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