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pro vyhledávání: '"Saunders, B. David"'
One useful standard method to compute eigenvalues of matrix polynomials ${\bf P}(z) \in \mathbb{C}^{n\times n}[z]$ of degree at most $\ell$ in $z$ (denoted of grade $\ell$, for short) is to first transform ${\bf P}(z)$ to an equivalent linear matrix
Externí odkaz:
http://arxiv.org/abs/2102.09726
We determine the probability, structure dependent, that the block Wiedemann algorithm correctly computes leading invariant factors. This leads to a tight lower bound for the probability, structure independent. We show, using block size slightly large
Externí odkaz:
http://arxiv.org/abs/1803.03864
Publikováno v:
In Journal of Symbolic Computation January-February 2022 108:98-116
Blackbox algorithms for linear algebra problems start with projection of the sequence of powers of a matrix to a sequence of vectors (Lanczos), a sequence of scalars (Wiedemann) or a sequence of smaller matrices (block methods). Such algorithms usual
Externí odkaz:
http://arxiv.org/abs/1412.5071
We describe in this paper new design techniques used in the \cpp exact linear algebra library \linbox, intended to make the library safer and easier to use, while keeping it generic and efficient. First, we review the new simplified structure for con
Externí odkaz:
http://arxiv.org/abs/1407.3262
We present algorithms to compute the Smith Normal Form of matrices over two families of local rings. The algorithms use the \emph{black-box} model which is suitable for sparse and structured matrices. The algorithms depend on a number of tools, such
Externí odkaz:
http://arxiv.org/abs/1201.5365
Publikováno v:
The Third International Congress on Mathematical Software, Kobe : Japan (2010)
To maximize efficiency in time and space, allocations and deallocations, in the exact linear algebra library \linbox, must always occur in the founding scope. This provides a simple lightweight allocation model. We present this model and its usage fo
Externí odkaz:
http://arxiv.org/abs/1009.1317
Publikováno v:
(International Symposium on Symbolic and Algebraic Computation 2009), S\'eoul : Cor\'ee, R\'epublique de (2009)
We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial. The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to matrices
Externí odkaz:
http://arxiv.org/abs/0901.4747
Publikováno v:
In Journal of Symbolic Computation May-June 2016 74:55-69
Autor:
Saunders, B. David, Schneider, Hans
Publikováno v:
SIAM Review, 1979 Oct 01. 21(4), 528-541.
Externí odkaz:
https://www.jstor.org/stable/2030106