3-Ma’ruza: Chiziqli algebraik tenglamalar sistemasini taqribiy yechish Reja

3.9 - Maple 7 dasturi
Oddiy iteratsiya usulida chiziqli tenglamalar sistemasini yechimini topish(3.17-masala).
> with(LinearAlgebra):
> S := Matrix([[29.9,1.2,2.1,0.9],[1.2,21.2,1.5,2.5], [2.1,1.5,19.8,1.3],[0.9,2.5,1.3,32.1]], datatype=float, storage=sparse):
t := Vector([21.7,27.46,28.76,49.72], datatype=float):
LinearSolve(S, t, method='SparseIterative');
0.55667424469169191
1.01144966965007299
1.22461595523565592
1.40493359077402147

Oddiy iteratsiya usuli asosida chiziqli tenglamalar sistemasining hisoblash dasturini tuzamiz:

{ * --3.11- Paskal tilida dastur - *}
uses crt;
label 40,90,100;
var
n,i,j:integer;
c,c1:real;
a:array[1..5,1..5] of real;
b:array[1..5] of real;
x:array[1..5] of real;
x1:array[1..5] of real;
begin
clrscr;
writeln(' Oddiy iteratsiya usulida ');
writeln(‘ chiziqli tenglamalar sistemasini yechish’);
write('tenglamalar soni N=');
readln(n);
for i:=1 to n do
begin
for j:=1 to n do
begin
gotoxy(16*j,4*i);
write(‘a[‘,i,’:’,j,’]=’);
read(a[i,j]);
end;
gotoxy(22*j,4*i);
write(‘b[‘,i,’]=’);
read(b[i]);
end;
for i:=1 to n do
begin
c:=a[i,i];
for j:=1 to n do a[i,j]:=a[i,j]/c;
b[i]:=b[i]/c;
x[i]:=b[i];
end;
40: for i:=1 to n do a[i,i]:=0;
for i:=1 to n do
begin
c1:=0;
for j:=1 to n do c1:=c1+a[i,j]*x[j];
x1[i]:=b[i]-c1;
end;
for i:=1 to n do
if abs(x[i]-x1[i])>0.01 then goto 90;