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| author | priyanka | 2015-06-24 15:03:17 +0530 |
|---|---|---|
| committer | priyanka | 2015-06-24 15:03:17 +0530 |
| commit | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch) | |
| tree | ab291cffc65280e58ac82470ba63fbcca7805165 /50/CH4/EX4.38 | |
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initial commit / add all books
Diffstat (limited to '50/CH4/EX4.38')
| -rwxr-xr-x | 50/CH4/EX4.38/ex_4_38.sce | 26 |
1 files changed, 26 insertions, 0 deletions
diff --git a/50/CH4/EX4.38/ex_4_38.sce b/50/CH4/EX4.38/ex_4_38.sce new file mode 100755 index 000000000..96d5857a9 --- /dev/null +++ b/50/CH4/EX4.38/ex_4_38.sce @@ -0,0 +1,26 @@ +// example 4.38
+// gram schmidt orthogonalisation
+
+W=1;
+ x=poly(0,"x");
+ P0=1;
+ phi0=P0;
+ a10=integrate('W*x*phi0','x',0,1)/integrate('W*1*phi0','x',0,1)
+ P1=x-a10*phi0
+ phi1=P1;
+
+ a20=integrate('W*x^2*phi0','x',0,1)/integrate('W*1*phi0','x',0,1)
+
+ a21=integrate('(x^2)*(x-1/2)','x',0,1)/integrate('(x-1/2)^2','x',0,1)
+
+ P2=x^2-a20*x-a21*phi1
+
+// since ,I= intgral [x^(1/2)-c0*P0-c1*P1-c2*P2]^2 inthe range [0,1]
+
+// hence partially derivating I
+
+c0=integrate('x^(1/2)','x',0,1)/integrate('1','x',0,1)
+c1=integrate('(x^(1/2))*(x-(1/2))','x',0,1)/integrate('(x-(1/2))^2','x',0,1)
+c1=integrate('(x^(1/2))*(x^2-4*x/3+1/2)','x',0,1)/integrate('(x^2-4*x/3+1/2)^2','x',0,1)
+
+
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