Some vector sequence transformations with applications to systems of equations
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First, recursive algorithms for implementing some vector sequence transformations are given. In a particular case, these transformations are generalizations of Shanks transformation and the G-transformation. When the sequence of vectors under transformation is generated by linear fixed point iterations, Lanczos' method and the CGS are recovered respectively. In the case of a sequence generated by nonlinear fixed point iterations, a quadratically convergent method based on the ε-algorithm is recovered and a nonlinear analog of the CGS method is obtained.
Subject classificationAMS (MOS) 65B05 65F10 65F25
KeywordsVector sequence extrapolation Lanczos method
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