Introduction to Iterative Methods: Part 1 Exercises
Problem on Page 2 of notes:
restart: with(LinearAlgebra):
Aaug:=Matrix(2,3,[[1.0,1.0,0.0],[1.0,1.0012,1.0]]);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkqbXZlcmJhdGltR0YkNiNRKCUlQWF1Z0dGJy1JI21vR0YkNi1RIzo9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1FbXXQtSShtZmVuY2VkRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNigtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNiMtSSdtdGFibGVHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2Ni1JJG10ckc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjYoLUkkbXRkRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNigtSSNtbkc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjYkUSQxLjA2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiIvJSlyb3dhbGlnbkdRITYiLyUsY29sdW1uYWxpZ25HUSE2Ii8lK2dyb3VwYWxpZ25HUSE2Ii8lKHJvd3NwYW5HUSIxNiIvJStjb2x1bW5zcGFuR1EiMTYiLUkkbXRkRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNigtSSNtbkc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjYkUSQxLjA2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiIvJSlyb3dhbGlnbkdRITYiLyUsY29sdW1uYWxpZ25HUSE2Ii8lK2dyb3VwYWxpZ25HUSE2Ii8lKHJvd3NwYW5HUSIxNiIvJStjb2x1bW5zcGFuR1EiMTYiLUkkbXRkRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNigtSSNtbkc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjYkUSMwLjYiLyUsbWF0aHZhcmlhbnRHUSdub3JtYWw2Ii8lKXJvd2FsaWduR1EhNiIvJSxjb2x1bW5hbGlnbkdRITYiLyUrZ3JvdXBhbGlnbkdRITYiLyUocm93c3BhbkdRIjE2Ii8lK2NvbHVtbnNwYW5HUSIxNiIvJSlyb3dhbGlnbkdRITYiLyUsY29sdW1uYWxpZ25HUSE2Ii8lK2dyb3VwYWxpZ25HUSE2Ii1JJG10ckc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjYoLUkkbXRkRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNigtSSNtbkc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjYkUSQxLjA2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiIvJSlyb3dhbGlnbkdRITYiLyUsY29sdW1uYWxpZ25HUSE2Ii8lK2dyb3VwYWxpZ25HUSE2Ii8lKHJvd3NwYW5HUSIxNiIvJStjb2x1bW5zcGFuR1EiMTYiLUkkbXRkRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNigtSSNtbkc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjYkUScxLjAwMTI2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiIvJSlyb3dhbGlnbkdRITYiLyUsY29sdW1uYWxpZ25HUSE2Ii8lK2dyb3VwYWxpZ25HUSE2Ii8lKHJvd3NwYW5HUSIxNiIvJStjb2x1bW5zcGFuR1EiMTYiLUkkbXRkRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNigtSSNtbkc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjYkUSQxLjA2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiIvJSlyb3dhbGlnbkdRITYiLyUsY29sdW1uYWxpZ25HUSE2Ii8lK2dyb3VwYWxpZ25HUSE2Ii8lKHJvd3NwYW5HUSIxNiIvJStjb2x1bW5zcGFuR1EiMTYiLyUpcm93YWxpZ25HUSE2Ii8lLGNvbHVtbmFsaWduR1EhNiIvJStncm91cGFsaWduR1EhNiIvJSZhbGlnbkdRJWF4aXM2Ii8lKXJvd2FsaWduR1EpYmFzZWxpbmU2Ii8lLGNvbHVtbmFsaWduR1EnY2VudGVyNiIvJStncm91cGFsaWduR1EnfGdyZnJsZWZ0fGdyaHI2Ii8lL2FsaWdubWVudHNjb3BlR1EldHJ1ZTYiLyUsY29sdW1ud2lkdGhHUSVhdXRvNiIvJSZ3aWR0aEdRJWF1dG82Ii8lK3Jvd3NwYWNpbmdHUSYxLjBleDYiLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtNiIvJSlyb3dsaW5lc0dRJW5vbmU2Ii8lLGNvbHVtbmxpbmVzR1Elbm9uZTYiLyUmZnJhbWVHUSVub25lNiIvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbXxpcjAuNWV4NiIvJSplcXVhbHJvd3NHUSZmYWxzZTYiLyUtZXF1YWxjb2x1bW5zR1EmZmFsc2U2Ii8lLWRpc3BsYXlzdHlsZUdRJmZhbHNlNiIvJSVzaWRlR1EmcmlnaHQ2Ii8lMG1pbmxhYmVsc3BhY2luZ0dRJjAuOGVtNiIvJSxtYXRodmFyaWFudEdRJ25vcm1hbDYiL0krbXNlbWFudGljc0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IlEnTWF0cml4NiIvJSVvcGVuR1EiWzYiLyUmY2xvc2VHUSJdNiIvSSttc2VtYW50aWNzRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiUSdNYXRyaXg2IkYn
RRE_A:=ReducedRowEchelonForm(Aaug);
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
Aaug:=Matrix(2,3,[[1.0,1.0,0.0],[1.0,1.001,1.0]]);
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
RRE_A:=ReducedRowEchelonForm(Aaug);
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
Aaug:=Matrix(2,3,[[1.0,1.0,0.0],[1.0,1.00,1.0]]);
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
RRE_A:=ReducedRowEchelonForm(Aaug);
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
Problem on Page 3 of notes
restart: with(LinearAlgebra):
Baug:=Matrix(2,3,[[4.552,7.083,1.931],[1.731,2.69,2.001]]);
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
RRE_B:=ReducedRowEchelonForm(Baug);
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
Baug:=Matrix(2,3,[[4.6,7.1,1.9],[1.7,2.7,2.0]]);
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
RRE_B:=ReducedRowEchelonForm(Baug);
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
Baug[1,1]/Baug[1,2];
JCIrUksoKXlrISM1
Baug[2,1]/Baug[2,2];
JCIrJ0gnSCdIJyEjNQ==
Jacobi Iteration: starting page 3 of notes
restart:
with(LinearAlgebra):
fcn1:=x->(5+x)/7;fcn2:=x->(7+3*x)/5;x1[0]:=0.;x2[0]:=0.;
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYjIiImIiIoIiIiOSQjRi1GLEYlRiVGJQ==
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYjIiIoIiImIiIiOSQjIiIkRixGJUYlRiU=
JCIiIUYj
JCIiIUYj
for i from 1 by 1 to 6 do im1:=i-1: x1[i]:=evalf(fcn1(x2[im1]),4): x2[i]:=evalf(fcn2(x1[im1]),4): end do;
IiIh
JCIlVnIhIiU=
JCIlKzkhIiQ=
IiIi
JCIlViIqISIl
JCIlSD0hIiQ=
IiIj
JCIlYygqISIl
JCIlXD4hIiQ=
IiIk
JCIlRioqISIl
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IiIl
JCIleioqISIl
JCIlJyo+ISIk
IiIm
JCIlJSoqKiEiJQ==
JCIlKio+ISIk
Aaug:=Matrix(2,3,[[7,-1,5],[3,-5,-7]]);
LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKCNwV0s=
RRE_A:=ReducedRowEchelonForm(Aaug);
LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKCFRc0s=
Gauss-Seidel Iteration: starts page 5
restart:
with(LinearAlgebra):
fcn1:=x->(5+x)/7;fcn2:=x->(7+3*x)/5;x1[0]:=0.;x2[0]:=0.;
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYjIiImIiIoIiIiOSQjRi1GLEYlRiVGJQ==
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYjIiIoIiImIiIiOSQjIiIkRixGJUYlRiU=
JCIiIUYj
JCIiIUYj
for i from 1 by 1 to 6 do im1:=i-1: x1[i]:=evalf(fcn1(x2[im1]),4): x2[i]:=evalf(fcn2(x1[i]),4): end do;
IiIh
JCIlVnIhIiU=
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IiIi
JCIlYygqISIl
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IiIk
JCIlKioqKiEiJQ==
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IiIl
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Second Gauss-Seidel system: bottom of page 5 of notes
fcn1:=x->(1+x)/1;fcn2:=x->(5-2*x)/1;x1[0]:=0.;x2[0]:=0.;
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYiIiJGKjkkRipGJUYlRiU=
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYiIiYiIiI5JCEiI0YlRiVGJQ==
JCIiIUYj
JCIiIUYj
for i from 1 by 1 to 6 do im1:=i-1: x1[i]:=evalf(fcn1(x2[im1]),4): x2[i]:=evalf(fcn2(x1[i]),4): end do;
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JCIiIiIiIQ==
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JCIiJSIiIQ==
JCEiJCIiIQ==
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JCEiIyIiIQ==
JCIiKiIiIQ==
IiIk
JCIjNSIiIQ==
JCEjOiIiIQ==
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JCEjOSIiIQ==
JCIjTCIiIQ==
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Note that if we rearrange the order of the two equations we have the following system:
fcn1:=x->(5-x)/2;fcn2:=x->(-1+1*x)/1;x1[0]:=0.;x2[0]:=0.;
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYjIiImIiIjIiIiOSQjISIiRixGJUYlRiU=
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYhIiIiIiI5JEYrRiVGJUYl
JCIiIUYj
JCIiIUYj
for i from 1 by 1 to 6 do im1:=i-1: x1[i]:=evalf(fcn1(x2[im1]),4): x2[i]:=evalf(fcn2(x1[i]),4): end do;
IiIh
JCIlK0QhIiQ=
JCIlKzohIiQ=
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JCIlXTwhIiQ=
JCIkXSghIiQ=
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JCIlRDYhIiQ=
IiIk
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IiIm
JCIlJSk+ISIk
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Unlike the first attempt, this attempt appears to be converging on a solution where x1 = 2 and x2 = 1.
Thus, rearranging the equations has an impact on convergence. Further, although the Theorem requires strict diagonal dominance to guarantee convergence, we see from this rearrangement that a system may converge without strict diagonal dominance (or as the disastrous first attempt shows, may not).
Solving exactly below, we see that the guess made from the second iteration attempt was appropriate.
Aaug:=Matrix(2,3,[[1,-1,1],[2,1,5]]);
LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKCcqb1gj
RRE_A:=ReducedRowEchelonForm(Aaug);
LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKCs0Ikg=
Problem 1: page 6 of notes
restart:
with(LinearAlgebra):
Jacobi Iteration
fcn1:=(y,z)->(17-y+z)/20;fcn2:=(x,z)->(13-x-z)/(-10);fcn3:=(x,y)->(18+x-y)/10;x1[0]:=0.;x2[0]:=0.;x3[0]:=0.;
Zio2JEkieUc2IkkiekdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgjIiM8IiM/IiIiOSQjISIiRi05JSNGLkYtRiVGJUYl
Zio2JEkieEc2IkkiekdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgjISM4IiM1IiIiOSQjRi5GLTklRjBGJUYlRiU=
Zio2JEkieEc2IkkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgjIiIqIiImIiIiOSQjRi4iIzU5JSMhIiJGMUYlRiVGJQ==
JCIiIUYj
JCIiIUYj
JCIiIUYj
for i from 1 by 1 to 6 do im1:=i-1: x1[i]:=evalf(fcn1(x2[im1],x3[im1]),4): x2[i]:=evalf(fcn2(x1[im1],x3[im1]),4): x3[i]:=evalf(fcn3(x1[im1],x2[im1]),4): end do;
IiIh
JCIlKyYpISIl
JCElKzghIiQ=
JCIlKz0hIiQ=
IiIi
JCIlMDUhIiQ=
JCElTjUhIiQ=
JCIlOj8hIiQ=
IiIj
JCIlLjUhIiQ=
JCElJikqKiEiJQ==
JCIlLz8hIiQ=
IiIk
JCIlKzUhIiQ=
JCElJyoqKiEiJQ==
JCIlKz8hIiQ=
IiIl
JCIlKzUhIiQ=
JCElKzUhIiQ=
JCIlKz8hIiQ=
IiIm
JCIlKzUhIiQ=
JCElKzUhIiQ=
JCIlKz8hIiQ=
Gauss-Seidel Iteration
fcn1:=(y,z)->(17-y+z)/20;fcn2:=(x,z)->(13-x-z)/(-10);fcn3:=(x,y)->(18+x-y)/10;x1[0]:=0.;x2[0]:=0.;x3[0]:=0.;
Zio2JEkieUc2IkkiekdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgjIiM8IiM/IiIiOSQjISIiRi05JSNGLkYtRiVGJUYl
Zio2JEkieEc2IkkiekdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgjISM4IiM1IiIiOSQjRi5GLTklRjBGJUYlRiU=
Zio2JEkieEc2IkkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgjIiIqIiImIiIiOSQjRi4iIzU5JSMhIiJGMUYlRiVGJQ==
JCIiIUYj
JCIiIUYj
JCIiIUYj
for i from 1 by 1 to 6 do im1:=i-1: x1[i]:=evalf(fcn1(x2[im1],x3[im1]),4): x2[i]:=evalf(fcn2(x1[i],x3[im1]),4): x3[i]:=evalf(fcn3(x1[i],x2[i]),4): end do;
IiIh
JCIlKyYpISIl
JCElOjchIiQ=
JCIlMT8hIiQ=
IiIi
JCIlNjUhIiQ=
JCElJSkqKiEiJQ==
JCIlLD8hIiQ=
IiIj
JCIlKioqKiEiJQ==
JCElKioqKiEiJQ==
JCIlKz8hIiQ=
IiIk
JCIlKzUhIiQ=
JCElKzUhIiQ=
JCIlKz8hIiQ=
IiIl
JCIlKzUhIiQ=
JCElKzUhIiQ=
JCIlKz8hIiQ=
IiIm
JCIlKzUhIiQ=
JCElKzUhIiQ=
JCIlKz8hIiQ=
Exact Solution
Aaug:=Matrix(3,4,[[20,1,-1,17],[1,-10,1,13],[-1,1,10,18]]);
LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKF8iZUc=
RRE_A:=ReducedRowEchelonForm(Aaug);
LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKENGSCQ=
Problem 2: page 6 of notes
restart:
with(LinearAlgebra):
Jacobi Iteration
fcn1:=(y)->(1+y)/3;fcn2:=(x,z)->(0+x+z)/3;fcn3:=(y,w)->(1+y+w)/10;fcn4:=(z)->(1+z)/3;x1[0]:=0.;x2[0]:=0.;x3[0]:=0.;x4[0]:=0.;
Zio2I0kieUc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYjIiIiIiIkRis5JEYqRiVGJUYl
Zio2JEkieEc2IkkiekdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCY5JCMiIiIiIiQ5JUYsRiVGJUYl
Zio2JEkieUc2Ikkid0dGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgjIiIiIiM1Riw5JEYrOSVGK0YlRiVGJQ==
Zio2I0kiekc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYjIiIiIiIkRis5JEYqRiVGJUYl
JCIiIUYj
JCIiIUYj
JCIiIUYj
JCIiIUYj
for i from 1 by 1 to 12 do im1:=i-1: x1[i]:=evalf(fcn1(x2[im1]),4): x2[i]:=evalf(fcn2(x1[im1],x3[im1]),4): x3[i]:=evalf(fcn3(x2[im1],x4[im1]),4): x4[i]:=evalf(fcn4(x3[im1]),4): end do;
IiIh
JCIlTEwhIiU=
JCIiIUYj
JCIlKzUhIiU=
JCIlTEwhIiU=
IiIi
JCIlTEwhIiU=
JCIlVzkhIiU=
JCIlTDghIiU=
JCIlbU8hIiU=
IiIj
JCIlOVEhIiU=
JCIlYjohIiU=
JCIlNjohIiU=
JCIleFAhIiU=
IiIk
JCIlXlEhIiU=
JCIldjwhIiU=
JCIlTTohIiU=
JCIlUFEhIiU=
IiIl
JCIlRFIhIiU=
JCIlJnoiISIl
JCIlaTohIiU=
JCIlV1EhIiU=
IiIm
JCIlSlIhIiU=
JCIlSD0hIiU=
JCIlazohIiU=
JCIlYVEhIiU=
IiIn
JCIlVlIhIiU=
JCIlSj0hIiU=
JCIlbzohIiU=
JCIlYVEhIiU=
IiIo
JCIlVlIhIiU=
JCIlUD0hIiU=
JCIlbzohIiU=
JCIlY1EhIiU=
IiIp
JCIlWFIhIiU=
JCIlUD0hIiU=
JCIlcTohIiU=
JCIlY1EhIiU=
IiIq
JCIlWFIhIiU=
JCIlUT0hIiU=
JCIlcTohIiU=
JCIlY1EhIiU=
IiM1
JCIlWVIhIiU=
JCIlUT0hIiU=
JCIlcTohIiU=
JCIlY1EhIiU=
IiM2
JCIlWVIhIiU=
JCIlUT0hIiU=
JCIlcTohIiU=
JCIlY1EhIiU=
Gauss-Seidel Iteration
fcn1:=(y)->(1+y)/3;fcn2:=(x,z)->(0+x+z)/3;fcn3:=(y,w)->(1+y+w)/10;fcn4:=(z)->(1+z)/3;x1[0]:=0.;x2[0]:=0.;x3[0]:=0.;x4[0]:=0.;
Zio2I0kieUc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYjIiIiIiIkRis5JEYqRiVGJUYl
Zio2JEkieEc2IkkiekdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCY5JCMiIiIiIiQ5JUYsRiVGJUYl
Zio2JEkieUc2Ikkid0dGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgjIiIiIiM1Riw5JEYrOSVGK0YlRiVGJQ==
Zio2I0kiekc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYjIiIiIiIkRis5JEYqRiVGJUYl
JCIiIUYj
JCIiIUYj
JCIiIUYj
JCIiIUYj
for i from 1 by 1 to 7 do im1:=i-1: x1[i]:=evalf(fcn1(x2[im1]),4): x2[i]:=evalf(fcn2(x1[i],x3[im1]),4): x3[i]:=evalf(fcn3(x2[i],x4[im1]),4): x4[i]:=evalf(fcn4(x3[i]),4): end do;
IiIh
JCIlTEwhIiU=
JCIlNjYhIiU=
JCIlNjYhIiU=
JCIlLlAhIiU=
IiIi
JCIlLlAhIiU=
JCIlLzshIiU=
JCIlSTohIiU=
JCIlVlEhIiU=
IiIj
JCIlb1EhIiU=
JCIlKnoiISIl
JCIlazohIiU=
JCIlYVEhIiU=
IiIk
JCIlTFIhIiU=
JCIlSz0hIiU=
JCIlbzohIiU=
JCIlY1EhIiU=
IiIl
JCIlV1IhIiU=
JCIlUT0hIiU=
JCIlcTohIiU=
JCIlY1EhIiU=
IiIm
JCIlWVIhIiU=
JCIlUT0hIiU=
JCIlcTohIiU=
JCIlY1EhIiU=
IiIn
JCIlWVIhIiU=
JCIlUT0hIiU=
JCIlcTohIiU=
JCIlY1EhIiU=
Exact Solution
Aaug:=Matrix(4,5,[[3,-1,0,0,1],[-1,3,-1,0,0],[0,-1,10,-1,1],[0,0,-1,3,1]]);
LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKCUpPlsk
RRE_A:=ReducedRowEchelonForm(Aaug);
LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKG9AMSQ=
evalf(RRE_A,4);
LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciJytMKSo=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= TTdSMApJNFJUQUJMRV9TQVZFLzM0ODE5ODRYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISM1IiUiJiIiJCEiIiIiIUYpRihGJ0YoRilGKUYoIiM1RihGKUYpRihGJyIiIkYpRitGK0Ym TTdSMApJNFJUQUJMRV9TQVZFLzMwNjIxNjhYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISM1IiUiJiIiIiIiIUYoRihGKEYnRihGKEYoRihGJ0YoRihGKEYoRicjIiMpKSIkQiMjIiNURisjIiNORisjIiMnKUYrRiY= TTdSMApJM1JUQUJMRV9TQVZFLzk4MzMwMFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzUiJSImJCIiIiIiISRGKUYpRipGKkYqRidGKkYqRipGKkYnRipGKkYqRipGJyQiJVlSISIlJCIlUj1GLSQiJXE6Ri0kIiVkUUYtRiY=