Differentiation of Kaltofen's division-free determinant algorithm - Computer Science > Symbolic ComputationReport as inadecuate




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Abstract: Kaltofen has proposed a new approach in Kaltofen 1992 for computing matrixdeterminants. The algorithm is based on a baby steps-giant steps constructionof Krylov subspaces, and computes the determinant as the constant term of acharacteristic polynomial. For matrices over an abstract field and by theresults of Baur and Strassen 1983, the determinant algorithm, actually astraight-line program, leads to an algorithm with the same complexity forcomputing the adjoint of a matrix Kaltofen 1992. However, the latter isobtained by the reverse mode of automatic differentiation and somehow is not``explicit-. We study this adjoint algorithm, show how it can be implementedwithout resorting to an automatic transformation, and demonstrate its use onpolynomial matrices.



Author: Gilles Villard LIP

Source: https://arxiv.org/



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