Experiments in Mathematics

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Experiments in Mathematics
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MATLAB
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??????MATLAB??
??gauss???,gauss?? function A,ugauss(a,n) for
k1n-1 ???? for ik1n for
jk1n1 ??a(k,k)0,????? if
abs(a(k,k))gt1e-6 ???k??????
a(i,j)a(i,j)-a(i,k)/a(k,k)a(k,j)
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else a(k,k)0,??gauss????
disp('??gauss????') pause
exit end end
end end ???? x(n)a(n,n1)/a(n,n)
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for in-1-11 s0 for ji1n
ssa(i,j)x(j) end x(i)(a(i,n1)-s)/a(i,i
) end ??gauss???????? Atriu(a) ??????? ux
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????????MATLAB??
???gauss???? function A,ugauss(a,n) ???? for
k1n-1 ??? c0 for qkn if
abs(a(q,k))gtc ca(q,k) lq
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end end ?????0,???A??? if
abs(c)lt1e-10 disp('error') pause
exit end ??l???k,????l???k? if lk
for qkn1
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tempa(k,q) a(k,q)a(l.q)
a(l,q)temp end end ???k?????
for ik1n for jk1n
a(i,j)a(i,j)-a(i,k)/a(k,k)a(k,j) end
end
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end ???? x(n)a(n,n1)/a(n,n) for in-1-11
s0 for ji1n ssa(i,j)x(j)
end x(i)(a(i,n1)-s)/a(i,i) end
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?????gauss???????? Atriu(a) ??????? ux
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2????(Jacobian)?????
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Jacobian???MATLAB??
function x,spjac(a,b,n,x1) ?? eones(n,1) ??
???? x2zeros(n,1) ????? k0 ?????????????? wh
ile norm(e,2)gt1e-6 ??5???????
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if (rem(k,5)0) strsprintf('Xd g g g
g\n',k,x1) disp(str) end kk1
??x2(i) for i1n s0 for j1n
ssa(i,j)x1(j) end
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x2(i)(b(i)-s)/a(i,i)x1(i) end ??????
ex2-x1 ?x2???????? x1x2 end ?????? sp
k ????? xx2
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?3???Jacobian????????
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2???-???(Gauss-Seidel)?????
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4????(Successive Over Relaxation method)???
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