Searching for authors named "Wayne Eberly" – sorted by Relevance.
15 documents found, showing 1 through 10.
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Efficient Computations of Frobenius Forms over Small Fields
- …A new randomized algorithm is presented for computation of the Frobenius form of an nn matrix over a eld. A version of the algorithm is presented that uses standard arithmetic whose asymptotic expected complexity matches the worst case complexity of the best known deterministic algorithmic for this …
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Efficient Parallel Computations for Singular Band Matrices
- …. Efficient parallel algorithms are presented for singular band matrix computations over arbitrary fields --- including solving systems of linear equations, and computation of the rank and a maximal nonsingular minor of a nonsingular band matrix. The algorithms are reasonably fast: for computations…
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Black Box Frobenius Decompositions over Small Fields (Extended Abstract)
- …A new randomized algorithm is presented for computation of the Frobenius form and transition matrix for an n × n matrix over a field. Using standard matrix and polynomial arithmetic, the algorithm has an asymptotic expected complexity that matches the worst case complexity of the best known de…
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Decomposition Of Algebras Over Finite Fields And Number Fields
- …We consider the boolean complexity of the decomposition of semi-simple algebras over finite fields and number fields.…
- Cited by 6 (2 self) – Add To MetaCart
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Decomposition Of Algebras Over R And C
- …We consider the boolean complexity of the decomposition of matrix algebras over C and R with bases consisting of matrices over a number field. Deterministic polynomial time algorithms for the decomposition of semi-simple algebras over these fields and Las Vegas polynomial time algorithms for the dec…
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Efficient Parallel Independent Subsets and Matrix Factorizations
- …A parallel algorithm is given for computation of a maximal linearly independent subset of a set of vectors over a field. The algorithm uses polylogarithmic time and uses a number of processors that differs by only a polylog factor from the number required for fast parallel matrix inversion. It is us…
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Asymptotically efficient algorithms for the Frobenius form
- …A new randomized algorithm is presented for computation of the Frobenius form of an nn matrix over a field. A version of the algorithm is presented that uses standard arithmetic whose asymptotic expected complexity matches the worst case complexity of the best known deterministic algorithm for this …
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On computing the determinant and Smith form of an integer matrix
- …A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix. For a matrix A ¡£ ¢ n ¤ n the algorithm requires O ¥ n 3 ¦ 5 ¥ logn § 4 ¦ 5 § bit operations (assuming for now that entries in A have constant size) using standard matrix and integer arithmetic. Using as…
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On Randomized Lanczos Algorithms
- …Las Vegas algorithms that are based on Lanczos's method for solving symmetric linear systems are presented and analyzed. These are compared to a similar randomized Lanczos algorithm that has been used for integer factorization, and to the (provably reliable) algorithm of Wiedemann. The analysis sugg…
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On Randomized Lanczos Algorithms
- …Las Vegas algorithms that are based on Lanczos's method for solving symmetric linear systems are presented and analyzed. These are compared to a similar randomized Lanczos algorithm that has been used for integer factorization, and to the (provably reliable) algorithm of Wiedemann. The analysis sugg…
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