Calculation of the characteristic polynomial of a matrix
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O. N. Pereslavtseva
Abstract
We consider efficient algorithms of calculation of the characteristic polynomials of matrices over commutative rings. We give estimates of complexity treated as the number of ring operations, and for the ring of integers the estimates are presented in terms of the number of multiplication operations over the machine words. We suggest a new algorithm to calculate the characteristic polynomial which has the best estimate of complexity in the ring operations. We give recommendations concerning applications of the algorithm of calculation of the characteristic polynomials depending on the size of the matrix, in particular, the algorithm suggested in this paper is recommended to be applied to integer-element matrices of size greater than 60.
© de Gruyter 2011
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Artikel in diesem Heft
- On the maximum size of a tree in a random unlabelled unrooted forest
- Asymptotic normality of the number of values of m-dependent random variables which occur a given number of times
- Limit theorems for the joint distribution of component sizes of a random mapping with a known number of components
- A combinatorial approach to calculation of moments of characteristics of runs in ternary Markov sequences
- The critical ω-foliated τ-closed formations of finite groups
- On the semigroups of endomorphisms of direct products of commutative Moufang loops
- The Voronoi polyhedra of the rooted lattice E6 and of its dual lattice
- Calculation of the characteristic polynomial of a matrix
- A case of insolubility of the problem of equivalence of programs
