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» Convergence of the Magnus Series
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FOCM
2008
88views more  FOCM 2008»
13 years 3 months ago
Convergence of the Magnus Series
The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals...
Per Christian Moan, Jitse Niesen
PE
2000
Springer
101views Optimization» more  PE 2000»
13 years 4 months ago
On the convergence of the power series algorithm
In this paper we study the convergence properties of the power series algorithm, which is a general method to determine (functions of) stationary distributions of Markov chains. W...
Gerard Hooghiemstra, Ger Koole
CASC
2010
Springer
149views Mathematics» more  CASC 2010»
13 years 3 months ago
Series Transformations to Improve and Extend Convergence
G. A. Kalugin, D. J. Jeffrey
ANTS
1998
Springer
135views Algorithms» more  ANTS 1998»
13 years 8 months ago
Fast Multiprecision Evaluation of Series of Rational Numbers
We describe two techniques for fast multiple-precision evaluation of linearly convergent series, including power series and Ramanujan series. The computation time for N bits is O(...
Bruno Haible, Thomas Papanikolaou