Summary
Generalized conjugate gradient algorithms which are invariant to a nonlinear scaling of a strictly convex quadratic function are described. The algorithms when applied to scaled quadratic functionsf∶R n →R 1 of the formf(x)=h(F(x)) withF(x) strictly convex quadratic andh∈C 1(R 1) an arbitrary strictly monotone functionh generate the same direction vectors as for the functionF without perfect steps.
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Abaffy, J., Sloboda, F. Imperfect conjugate gradient algorithms for extended quadratic functions. Numer. Math. 42, 97–105 (1983). https://doi.org/10.1007/BF01400920
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DOI: https://doi.org/10.1007/BF01400920