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By K. Yokoyama, K. Shirayanagi

This quantity covers probably the most fresh and important advances in desktop arithmetic, together with algebraic, symbolic, numeric and geometric computation, computerized mathematical reasoning, mathematical software program and computer-aided geometric layout. Researchers, engineers, teachers and graduate scholars attracted to doing arithmetic utilizing pcs should still locate this quantity reliable examining and a worthwhile reference.

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Extra resources for Computer Mathematics - Proceedings of the 5th Asian Symposium, ASCM 2001 (Lecture Notes Series on Computing)

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0, where Sj are the invariant factors of H, that is, nonconstant monic polynomials with the property that Sj is a (trivial or nontrivial) polynomial factor of S;_i for all 2 < i < (p. Because the Smith normal form of the characteristic matrix XI —A corresponds to the canonical forms (Frobenius, Jordan) for similarity to A, the largest invariant factor of XI — A, S\ (A), equals the minimum polynomial fA(X). Theorem 1 Let A G K n x n , X e Knxl, Y G K n x m and let s i , . . , s 0 denote all invariant factors of XI — A.

Compute the minimal matrix generator Fx' (A) for {B^}i>o- Step 4. Compute the leading and constant coefficients of A(A) = det(Fx' (A)). If deg(A) < n and A(0) ^ 0 then return "failure" else return det(^4) = A(0)/leading coefficient(A). For Step 2 we utilize our baby steps/giant steps technique of Section 2. Let the number of giant steps be s = \nT ] , where r = 1/3, and let the number of baby steps be r = \{2n/m + 3)/s] = 0(n1-'T-T). 3. For A: = 1 , 2 , . . 4. For j = 0 , 1 , . . , r - 1 Do For k = 0 , 1 , .

Brent, F. G. Gustavson, and D. Y. Y. Yun. Fast solution of Toeplitz systems of equations and computation of Pade approximants. J. Algorithms, 1:259-295, 1980. H. Bronnimann, I. Emiris, V. Pan, and S. Pion. Sign determination in residue number systems. Theoretical Comput. , 210(1):173-197, 1999. Special issue on real numbers and computers. H. Bronnimann and M. Yvinec. A complete analysis of Clarkson's algorithm for safe determinant evaluation. Technical Report INRIA2051, Institut National de Recherche en Informatique et en Automatique, Novembre 1996.

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