BiCGStab, VPAStab and an adaptation to mildly nonlinear systems

The key equations of BiCGStab are summarised to show its connections with Padé and vector-Padé approximation. These considerations lead naturally to stabilised vector-Padé approximation of a vector-valued function (VPAStab), and an algorithm for the acceleration of convergence of a linearly generate...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2007-04, Vol.201 (1), p.284-299
Main Author: Graves-Morris, P.R.
Format: Article
Language:English
Subjects:
Acceleration of convergence
Approximations and expansions
BiCGStab
Bratu equation
Burghers’ equation
Exact sciences and technology
Mathematical analysis
Mathematics
Nonlinear algebraic and transcendental equations
Nonlinear system
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Vector-Padé approximation
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Summary:The key equations of BiCGStab are summarised to show its connections with Padé and vector-Padé approximation. These considerations lead naturally to stabilised vector-Padé approximation of a vector-valued function (VPAStab), and an algorithm for the acceleration of convergence of a linearly generated sequence of vectors. A generalisation of this algorithm for the acceleration of convergence of a nonlinearly generated system is proposed here, and comparative numerical results are given.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2006.02.022