D. Calvetti, E. Gallopoulas, and L. Reichel, Incomplete partial fractions for parallel evaluations of rational matrix functions, J. Comp. Appl. Math., vol. 59, pp. 349-380, 1995. 18 Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Evaluating Padé Approximants Of The Matrix Logarithm - Higham (2000) (Correct)
....j and fi (m) j are given in [6, App. 2] 16, Sec. 4.5] these computations are of negligible cost if m n and the coefficients can of course be precomputed and stored. The cost of evaluating (2.4) at the matrix X is mI . An advantage of (2. 4) is its suitability for parallel evaluation; see [4] for a discussion and extensive bibliography on parallel evaluation of matrix partial fraction expansions. Table 2.1 summarizes the cost of the methods. The Paterson Stockmeyer and Van Loan methods clearly require the least computation for large m, since their costs grow as p m for the optimal ....
....k k 1 [18] or kA=2 k k 1=2 [14] 8, Sec. 11.3] We briefly summarize some pertinent facts concerning the evaluation of r m (A=2 k ) The coefficients ff (m) j and fi (m) j in the partial fraction expansion (2. 4) of r m are not known explicitly, and the ff (m) j can be very large [4], leading to numerical instability in the evaluation of the expansion. However, the techniques of [4] can be used to obtain an incomplete partial fraction expansion with suitably bounded coefficients. Ill conditioning of the denominator polynomial q m is not an issue, as (q m (B) 5 for kBk 1 ....
[Article contains additional citation context not shown here]
D. Calvetti, E. Gallopoulos, and L. Reichel. Incomplete partial fractions for parallel evaluation of rational matrix functions. J. Comp. Appl. Math., 59:349--380, 1995.
Cyclic Reduction - History and Applications - Gander, Golub (Correct)
....we can express v = i A (r) j Gamma1 u = P 2 r (A) Gamma1 u = 2 r X i=1 c (r) i (A Gamma (k) i I) Gamma1 u where now the 2 r linear systems (A Gamma (k) i I) Gamma1 u in the sum may be computed independently and in parallel. As discussed by Calvetti et al. in [6], partial fraction expansion may be more sensitive to roundoff errors in the presence of close poles. 3.3 Buneman s Algorithm It has been observed that block Cyclic Reduction using the recurrence relation (25) g (r 1) j = g (r) 2j Gamma1 Gamma A (r) g (r) 2j g (r) 2j 1 ; j = 1; ....
Calvetti, D., Gallopoulos, E., Reichel, L.: Incomplete partial fractions for parallel evaluation of rational matrix functions. Journal of Computational and Applied Mathematics 59 (1995) 349--380
A Parallel Iterative Method for Exponential Propagation - Baldwin, Freund, Gallopoulos Self-citation (Gallopoulos) (Correct)
....experiments, and discuss the computational performance of the algorithm. 1 Problem Specification The computation of x : exp( GammaA)b; 1) where b is a vector and A is a real matrix of order N , possibly nonsymmetric, is an important kernel operation in several application areas; see, e.g. [1, 2, 5, 14] and the references given therein. For large A it becomes prohibitive to compute exp( GammaA) directly (e.g. based on a spectral decomposition of A) and alternative methods have to be used. One typical class of methods approximates x by x : R(A)b; where R(z) q(z) p(z) with polynomials p; ....
....Street, Urbana, IL 61801 (stratis csrd.uiuc.edu) Supported in part by the U.S. National Science Foundation grant No. NSF CCR 91 20105. 2 Baldwin et al. The formula (3) gives rise to the following Algorithm PF (Partial Fraction) for computing an approximation x to the sought vector x; see [1, 9]. Algorithm PF (Computation of approximation x to (1) using formulas (2) and (3) 1) Compute ff 0 = lim z 1 q(z) p(z) and ff j = q(z j ) p 0 (z j ) j = 1; 2; n; 2) For j = 1; 2; n, compute x j by solving (A Gamma z j I)x j = b; 4) 3) Set x = ff 0 b n X j=1 ....
[Article contains additional citation context not shown here]
D. Calvetti, E. Gallopoulos, and L. Reichel, Incomplete partial fractions for parallel evaluation of rational matrix functions, J. Comput. Appl. Math., to appear (1995).
Krylov Subspace Methods for Large-Scale Matrix Problems in Control - Datta (2002) (Correct)
No context found.
D. Calvetti, E. Gallopoulas, and L. Reichel, Incomplete partial fractions for parallel evaluations of rational matrix functions, J. Comp. Appl. Math., vol. 59, pp. 349-380, 1995. 18
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC