Minimum Polynomial Extrapolation for Convergence Matlab script

Publisher review:
Minimum Polynomial Extrapolation for Convergence Acceleration takes for input an n by k matrix of n-dimensional iterates The function s=MPE(X) extrapolates the limit of a sequence of vectors. It is similar to Aitken's delta squared process, which accelerates the convergence of linearly convergent iterations, often resulting in quadratically convergent iterations. However, Aitken's delta squared process is not effective on vector sequences. Usually, the sequence is given by a fixed point iteration, but the acceleration also sometimes works if the iteration is not in such a form.In typical uses, one would havex(:,1)=initial_guess;for j=1:max_iterfor k=1:3x(:,k 1)=f(x(:,k));endx=MPE(x);endThe function MPE must be provided with an n by k matrix, k must be at least 3. It may happen that better_x is not actually better. In this case, the calling function can detect it by noticing that the residual of MPE(x) is worse than the residual of x(:,end). The number k of iterates is often taken to be 3, but some problems may require a larger k. However, including some early, poor iterates may also result in a poorer acceleration, so typically one does not increase k arbitrarily.The attached graph shows the convergence behavior of MPE for the fixed point iteration forf=@(x) [((x(1)-1)^2 x(2)^2)/2;x(2)/2]; Requirements: · MATLAB Release: R2006a
Operating system:
Windows / Linux / Mac OS / BSD / Solaris

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