ISSN:
1436-4646
Keywords:
Path Following
;
PL Methods
;
Predictor—Corrector Algorithms
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We consider path following methods designed to trace the zeroes of a continuous or differentiable mapF:R n+1 →R n . These methods are applicable e.g. in the numerical study of nonlinear eigenvalue and bifurcation problems. Traditionally a simplicial algorithm is based on a fixed triangulationT ofR n+1 and a corresponding piecewise linear approximationF T :R n+1 →R n .4 A fixed triangulation algorithm then traces the zeroes ofF T via a complementary pivoting procedure. We present two kinds of hybrid algorithms that have the structure of a predictor—corrector method using simplicial methods to carry out the corrector steps. Numerical experience is reported showing the improvement in efficiency as compared to the fixed triangulation algorithm.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01583781
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