Kaltofen’s division-free determinant algorithm differentiated for matrix adjoint computation
نویسندگان
چکیده
منابع مشابه
Kaltofen's division-free determinant algorithm differentiated for matrix adjoint computation
Kaltofen has proposed a new approach in Kaltofen (1992) for computing matrix determinants without divisions. The algorithm is based on a baby steps/giant steps construction of Krylov subspaces, and computes the determinant as the constant term of the characteristic polynomial. For matrices over an abstract ring, by the results of Baur and Strassen (1983), the determinant algorithm, actually a s...
متن کاملDifferentiation of Kaltofen's division-free determinant algorithm
Kaltofen has proposed a new approach in [8] for computing matrix determinants. The algorithm is based on a baby steps/giant steps construction of Krylov subspaces, and computes the determinant as the constant term of a characteristic polynomial. For matrices over an abstract field and by the results of Baur and Strassen [1], the determinant algorithm, actually a straight-line program, leads to ...
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Abstract. The best method for computing the adjoint matrix of an order n matrix in an arbitrary commutative ring requires O(n log n log log n) operations, provided the complexity of the algorithm for multiplying two matrices is γn + o(n). For a commutative domain – and under the same assumptions – the complexity of the best method is 6γn/(2 − 2) + o(n). In the present work a new method is prese...
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We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointin...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2011
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2010.08.012