Příklad číslo 2
> with(CurveFitting):
>
P:=PolynomialInterpolation([9,3,4.5,10,5.5,12.5],[9+sin(9),3+sin(
3),4.5+sin(4.5),10+sin(10),5.5+sin(5.5),12.5+sin(12.5)],x,form=La
grange);
P 0.003023431595 ( )+9 ( )sin 9 ( )-x 3 ( )-x 4.5 ( )-x 10 ( )-x 5.5 ( )-x 12.5:=
0.0006683375104 ( )+3 ( )sin 3 ( )-x 9 ( )-x 4.5 ( )-x 10 ( )-x 5.5 ( )-x 12.50.01186016795
( )-x 9 ( )-x 3 ( )-x 10 ( )-x 5.5 ( )-x 12.5+
0.002308802309 ( )+10 ( )sin 10 ( )-x 9 ( )-x 3 ( )-x 4.5 ( )-x 5.5 ( )-x 12.50.01739486503
( )-x 9 ( )-x 3 ( )-x 4.5 ( )-x 10 ( )-x 12.50.002671037186
( )-x 9 ( )-x 3 ( )-x 4.5 ( )-x 10 ( )-x 5.5+
> expand(evalf(P));
3.09117021 x 2.21991775 x2
0.545203518 x3
0.0513743551 x4
- + 0.00166192229
x5
2.88384950+ +
>
plot([x+sin(x),P],x=0..15,color=[blue,red],thickness=3,legend=["P
ůvodní funkce","Lagrangeův polynom"]);
Příklad číslo 3 - pomocné výpočty
> with(linalg):
>
A:=linalg[matrix](4,4,[1,1,1,1,1024,256,64,16,5,4,3,2,1280,256,48
,8]);
:=A


















1 1 1 1
1024 256 64 16
5 4 3 2
1280 256 48 8
> B:=inverse(A);
:=B






































-4
27
-7
864
1
9
1
144
13
9
1
18
-1
-1
24
-40
9
-25
288
8
3
1
16
112
27
17
432
-16
9
-1
36
> a:=linalg[matrix](4,1,[2,-5,-2,1]);
:=a


















2
-5
-2
1
> linalg[multiply](B,a);






































-407
864
329
72
-3953
288
5023
432
Příklad číslo 4 - pomocné výpočty
>
C:=linalg[matrix](6,6,[1,1,0,0,0,0,0,0,1,1,1,1,0,0,27,9,3,1,3,1,-
3,-2,-1,0,6,0,-6,-2,0,0,0,0,18,2,0,0]);
:=C




























1 1 0 0 0 0
0 0 1 1 1 1
0 0 27 9 3 1
3 1 -3 -2 -1 0
6 0 -6 -2 0 0
0 0 18 2 0 0
> c:=linalg[matrix](6,1,[-1/2,1/2,1/10,0,0,0]);
:=c










































-1
2
1
2
1
10
0
0
0
> C1:=inverse(C);
:=C1




























































-1
6
-1
12
1
12
1
6
1
9
-1
18
7
6
1
12
-1
12
-1
6
-1
9
1
18
1
12
1
24
-1
24
-1
12
1
36
1
9
-3
4
-3
8
3
8
3
4
-1
4
-1
2
23
12
11
24
-11
24
-23
12
23
36
5
9
-5
4
7
8
1
8
5
4
-5
12
-1
6
> linalg[multiply](C1,c);




























































1
20
-11
20
-1
40
9
40
-31
40
43
40
Na příslušném intervalu:
> with(plots):
>
multiple(plot,[1/(1+x^2),x=0..3,color=red,thickness=3,legend="Pův
odní funkce"],[1-
11/20*x+1/20*x^3,x=0..1,color=blue,thickness=3,legend="S_0"],[43/
40-31/40*x+9/40*x^2-
1/40*x^3,x=1..3,color=green,thickness=3,legend="S_1"]);
Mimo něj:
> multiple(plot,[1/(1+x^2),x=5..7,color=red,thickness=3,legend="Původní
funkce"],[1-
11/20*x+1/20*x^3,x=-
5..4,color=blue,thickness=3,legend="S_0"],[43/40-
31/40*x+9/40*x^2-1/40*x^3,x=-
2..7,color=green,thickness=3,legend="S_1"]);
>