wxMaxima document 1 / 3

kill( all);
done
f ( x):=x^3+2·x^2−3·x−1;
3 2
f ( x ) := x + 2 x + − 3 x − 1
'x0=x0:1.0;
'x1=x1:2.0;
'n=n:8;
x0 = 1.0 x1 = 2.0 n=8
'err =err :0.0000001;
−7
err = 1.0 10
print( "itr","","root");
itr root root
'j =j :0;
j =0
for i:1 thru n do ( x2:( x1−( ( x1−x0)/ ( f ( x1)−f ( x0)))·f ( x1)),j :j +1,print( i,"",x2),
if ( abs( x2−x1)<err ) then ( print( "root cgs in",i,"iteration"), return( ))
else ( x0:x1,x1:x2));
print( "after root cgs in",j ,"root is",x2);
1 1.1
2 1.1517436380772856
3 1.203449860925807
4 1.1984799140986921
5 1.1986903248478271
6 1.1986912436939725
7 1.1986912435159969
root cgs in 7 iteration false
after root cgs in 7 root is 1.1986912435159969
1.1986912435159969
kill( all);
done
'x10=x10:0.0;
x10 = 0.0
'x20=x20:0.0;
x20 = 0.0
'x30=x30:0.0;
x30 = 0.0
wxMaxima document 2 / 3

for i:1 thru 8 do(

x1:( 10−x20−2·x30)/ 5,
x2:( −14+3·x10−4·x30)/ 9,
x3:( 33+x10+2·x20)/ 7,
print( i,"it gives","x1=",x1,"x2=",x2,"x3=",x3),
x10=x1,
x20=x2,
x30=x3);
print( "x1=",x1);
print( "x2=",x2);
print( "x3=",x3);
1 it gives x1= 2.0 x2= − 1.5555555555555556 x3=
4.714285714285714
2 it gives x1= 2.0 x2= − 1.5555555555555556 x3=
4.714285714285714
3 it gives x1= 2.0 x2= − 1.5555555555555556 x3=
4.714285714285714
4 it gives x1= 2.0 x2= − 1.5555555555555556 x3=
4.714285714285714
5 it gives x1= 2.0 x2= − 1.5555555555555556 x3=
4.714285714285714
6 it gives x1= 2.0 x2= − 1.5555555555555556 x3=
4.714285714285714
7 it gives x1= 2.0 x2= − 1.5555555555555556 x3=
4.714285714285714
8 it gives x1= 2.0 x2= − 1.5555555555555556 x3=
4.714285714285714 done
x1= 2.0 2.0
x2= − 1.5555555555555556 − 1.5555555555555556
x3= 4.714285714285714 4.714285714285714
kill( all);
done
'n=n:3;
n=3
'a=a:matrix( [ 5,1,2] ,[ 3,−9,−4] ,[ 1,2,−7] );
5 1 2

a= 3 −9 −4
1 2 −7

'b=b:matrix( [ 10] ,[ 14] ,[ −33] );

10

b = 14
− 33

'x=x:matrix( [ 0] ,[ 0] ,[ 0] );
wxMaxima document 3 / 3

x= 0
0

print( "itr","","","","","x1","","","","","x3","","","","","x3");
itr x1 x3 x3 x3
for k:1 thru 10 do( for i:1 thru n do(
y[ i] :float( ( b[ i] −sum( a[ i,j ] ·x[ j ] ,j ,1,i−1)−sum( a[ i,j ] ·x[ j ] ,j ,i+1,n))/ a[ i,i] )),
for i:1 thru n do( x[ i] :y[ i] ),
print( k,"","","",x[ 1] ,"","","",x[ 2] ,"","","",x[ 3] ));
for p:1 thru n do print( 'x[ p] :x[ p] );
1 [ 2.0 ] [ − 1.5555555555555556 ] [ 4.714285714285714 ]
2 [ 0.42539682539682533 ] [ − 2.984126984126984 ]
[ 4.555555555555555 ]
3 [ 0.7746031746031747 ] [ − 3.438447971781305 ]
[ 3.9224489795918362 ]
4 [ 1.1187100025195265 ] [ − 3.040665154950869 ]
[ 3.842529604434366 ]
5 [ 1.0711211892164276 ] [ − 2.8904431566865423 ]
[ 4.005339956088256 ]
6 [ 0.9759526489020062 ] [ − 2.9786662507448596 ]
[ 4.041462125120478 ]
7 [ 0.979148400100781 ] [ − 3.026443394863988 ]
[ 4.002660021058897 ]
8 [ 1.0042246705492388 ] [ − 3.0081327648814717 ]
[ 3.989465944338972 ]
9 [ 1.0058401752407056 ] [ − 2.9939099739675745 ]
[ 3.9982798772551846 ]
10 [ 0.9994700438914411 ] [ − 2.9972887759220694 ]
[ 4.002574318186507 ] done
[ 0.9994700438914411 ]
[ − 2.9972887759220694 ]
[ 4.002574318186507 ] done