This research project is an extension of the ASPN investigations looking for cycling behaviour in Schwarz methods preconditioned by Newton-Raphson.

Acceleration can be done by extrapolating from previous results, often improving speed up to quadratic convergence without significant increase in cost.

Some of this extrapolation can be posed as CG or other Krylov subspace methods.

Keywords:

--Method of Richardson

--Modified polynomial extrapolation (MPE)

--Conjugate gradient and Krylov subspace

Goals: --Arrive at a different method from Newton's (?)

--When is convergence quadratic?

--Apply such a method to the altS cyclic example

--Can all extrapolation methods be posed under a single unifying framework?

%--Images

Images are expected to be generated primarily through MATLAB experiments and TIKZ.

They will follow the naming convention:

FORMAT_extrap_SpecificTopic_v1_YYYYMMDD.svg

FORMAT: 3 to 4 letter indicator of how the file was created, ie. MTLB (MATLAB) or TIKZ.

extrap: indicates image is related to extrapolation research project.

SpecificTopic: identifies topic within research project the image relates to.

v1: version number.

YYYYMMDD: date of initial creation.

.svg: file format; use .eps for vector graphics when possible.

%--Code

Code is expected to be almost entirely MATLAB.

TYPE_extrap_Function_v1_YYYYMMDD.m

TYPE: 3 to 4 letters denoting intended result of the script:

PLOT: produces a plot, MTLB_extrap_Function_v1_YYYYMMDD.eps;