1 files changed, 104 insertions, 0 deletions
diff --git a/845/CH6/EX6.19/Ex6_19.sce b/845/CH6/EX6.19/Ex6_19.sce
new file mode 100755
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@@ -0,0 +1,104 @@
+//Example 6.19
+
+clc
+clear
+
+x = 0:4;
+n = length(x);
+f = "X^2 + Y^2 - Y";
+tab = %nan*ones(n,5);
+
+for j = 0:4
+    fj = strsubst(f,'Y','j');
+    for i = 1:n
+        tab(i,j+1) = eval(strsubst(fj,'X','x(i)'));
+    end
+end
+//tab(:,1) = [];
+mprintf("%4s %6s %6s %6s %6s %6s",'x','y=0','y=1','y=2','y=3','y=4')
+disp([(0:4)' tab])
+tab2 = tab(2:4,2:4)';
+n1 = length(tab2(:,1));
+y = 2:4;
+
+del1 = %nan*ones(n1,3);
+del1(:,1) = tab2(:,1);
+for j = 2:4
+    for i = 1:n1-j+1
+        del1(i,j) = del1(i+1,j-1) - del1(i,j-1);
+    end
+end
+
+del2 = %nan*ones(n1,3);
+del2(:,1) = tab2(:,2);
+for j = 2:4
+    for i = 1:n1-j+1
+        del2(i,j) = del2(i+1,j-1) - del2(i,j-1);
+    end
+end
+
+del3 = %nan*ones(n1,3);
+del3(:,1) = tab2(:,3);
+for j = 2:4
+    for i = 1:n1-j+1
+        del3(i,j) = del3(i+1,j-1) - del3(i,j-1);
+    end
+end
+
+y0 = y(1);
+Y = 3.5;
+hy = y(2) - y(1);
+py = (Y-y0)/hy;
+
+f1y = 0;
+del1y0 = del1(1,:);
+for i = 0:length(del1y0)-1
+    t = 1;
+    for j = 1:i
+        t = t * (py-j+1);
+    end
+    f1y = f1y + t*del1y0(i+1)/factorial(i);
+end
+
+f2y = 0;
+del2y0 = del2(1,:);
+for i = 0:length(del2y0)-1
+    t = 1;
+    for j = 1:i
+        t = t * (py-j+1);
+    end
+    f2y = f2y + t*del2y0(i+1)/factorial(i);
+end
+
+f3y = 0;
+del3y0 = del3(1,:);
+for i = 0:length(del3y0)-1
+    t = 1;
+    for j = 1:i
+        t = t * (py-j+1);
+    end
+    f3y = f3y + t*del3y0(i+1)/factorial(i);
+end
+
+del = %nan*ones(n1,3);
+del(:,1) = [f1y; f2y; f3y];
+for j = 2:4
+    for i = 1:n1-j+1
+        del(i,j) = del(i+1,j-1) - del(i,j-1);
+    end
+end
+
+f = 0;
+X = 2.5;
+x0 = x(2);
+hx = x(2) - x(1);
+px = (X-x0)/hx;
+del0 = del(1,:)
+for i = 0:length(del0)-1
+    t = 1;
+    for j = 1:i
+        t = t * (px-j+1);
+    end
+    f = f + t*del0(i+1)/factorial(i);
+end
+disp(f,"f(2.5,3.5) = ")