1 files changed, 27 insertions, 0 deletions
diff --git a/75/CH4/EX4.7/ex_6.sce b/75/CH4/EX4.7/ex_6.sce
new file mode 100755
index 000000000..b87b04d2a
--- /dev/null
+++ b/75/CH4/EX4.7/ex_6.sce
@@ -0,0 +1,27 @@
+        //    PG (219)
+
+deff('[y]=f(x)','y=exp(x)')
+
+x=-1:.01:1;                // defining the range of x
+
+//    Let r1(x) = b0 + b1(x)
+//    Minimize 
+//        ||f-r1||^2 = integrate('(exp(x)-b0-b1*x)^2','x',-1,1) = F(b0,b1)
+//    F = integrate('exp(2*x) + b0^2 + (b1^2)*(x^2) - 2*b0*x*exp(x) + 2*b0*b1*x','x',b0,b1)
+//    To find a minimum, we set
+
+//        df/db0 = 0
+//        df/db1 = 0-----------necessary conditions at a minimal point
+//    On solving, we get the values of b0 & b1
+
+b0 = 0.5*integrate('exp(x)','x',-1,1);
+b1 = 1.5*integrate('x*exp(x)','x',-1,1);
+r1 = b0+b1*x;
+norm(exp(x)-r1,'inf');    //    least squares approximation
+
+r3 = 0.996294 + 0.997955*x + 0.536722*x^2 + 0.176139*x^3; 
+norm(exp(x)-r3,'inf');    //    cubic least squares approximation
+
+//    average error E
+
+E = norm(exp(x)-r3,2)/sqrt(2)