Iterative Methods for Solving Linear Systems Suzanne Riehl restart: with(LinearAlgebra): with(plots): with(plottools):

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The basic objectives are: 1) Learn how to "program" a worksheet. 2) Find solutions to systems of equations iteratively using the Jacobi and the Gauss-Siedel methods 3) Plot intermediate solutions to see convergence/divergence of method.

A specific example. eq1:= 7*x-y=5; eq2:= 3*x-5*y = -7;

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solve(eq1,x),solve(eq2,y);

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Here's a procedure: nextJacobiPoint:=proc(pair0,eqn1, eqn2) local x1,y1: x1:=evalf(eval(solve(eq1,x),y=pair0[2])): y1 := evalf(eval(solve(eq2,y),x=pair0[1])): [x1,y1]: end proc: The procedure seems to work if pair0 contains integers. I don't know how to interpret result otherwise. nextJacobiPoint([5/7,0],eq1,eq2);

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NextPoint := nextJacobiPoint([0,0],eq1,eq2);

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NextPoint := nextJacobiPoint(NextPoint,eq1,eq2);

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The following block should generate points, which could then be plotted. listofpoints:=[[27,-13]]: for n from 1 to 10 do nextJacobiPoint(listofpoints[n],eq1,eq2): listofpoints:=[op(listofpoints),%]: end do: listofpoints;

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PointList := pointplot(listofpoints, connect=true,linestyle=DASH): LineList := plot({solve(eq1,y),solve(eq2,y)},x=-5..5): display({PointList, LineList});

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