added lecture 19

lecture_18/Newtint.m

@@ -1,33 +1,34 @@
-function yint = Newtint_bak(x,y,xx)
-% Newtint: Newton interpolating polynomial
-% yint = Newtint(x,y,xx): Uses an (n - 1)-order Newton
-%   interpolating polynomial based on n data points (x, y)
-%   to determine a value of the dependent variable (yint)
-%   at a given value of the independent variable, xx.
-% input:
-%   x = independent variable
-%   y = dependent variable
-%   xx = value of independent variable at which
-%        interpolation is calculated
-% output:
-%   yint = interpolated value of dependent variable
-
-% compute the finite divided differences in the form of a
-% difference table
-n = length(x);
-if length(y)~=n, error('x and y must be same length'); end
-b = zeros(n,n);
-% assign dependent variables to the first column of b.
-b(:,1) = y(:); % the (:) ensures that y is a column vector.
-for j = 2:n
-  for i = 1:n-j+1
-    b(i,j) = (b(i+1,j-1)-b(i,j-1))/(x(i+j-1)-x(i));
-  end
-end
-% use the finite divided differences to interpolate
-xt = 1;
-yint = b(1,1);
-for j = 1:n-1
-  xt = xt*(xx-x(j));
-  yint = yint+b(1,j+1)*xt;
-end
+function yint = Newtint(x,y,xx)
+% Newtint: Newton interpolating polynomial
+% yint = Newtint(x,y,xx): Uses an (n - 1)-order Newton
+%   interpolating polynomial based on n data points (x, y)
+%   to determine a value of the dependent variable (yint)
+%   at a given value of the independent variable, xx.
+% input:
+%   x = independent variable
+%   y = dependent variable
+%   xx = value of independent variable at which
+%        interpolation is calculated
+% output:
+%   yint = interpolated value of dependent variable
+
+% compute the finite divided differences in the form of a
+% difference table
+n = length(x);
+if length(y)~=n, error('x and y must be same length'); end
+b = zeros(n,n);
+% assign dependent variables to the first column of b.
+b(:,1) = y(:); % the (:) ensures that y is a column vector.
+for j = 2:n
+  for i = 1:n-j+1
+    b(i,j) = (b(i+1,j-1)-b(i,j-1))/(x(i+j-1)-x(i));
+  end
+end
+%b
+% use the finite divided differences to interpolate
+xt = 1;
+yint = b(1,1);
+for j = 1:n-1
+  xt = xt*(xx-x(j));
+  yint = yint+b(1,j+1)*xt;
+end

lecture_19/Newtint.m

@@ -0,0 +1,34 @@
+function yint = Newtint(x,y,xx)
+% Newtint: Newton interpolating polynomial
+% yint = Newtint(x,y,xx): Uses an (n - 1)-order Newton
+%   interpolating polynomial based on n data points (x, y)
+%   to determine a value of the dependent variable (yint)
+%   at a given value of the independent variable, xx.
+% input:
+%   x = independent variable
+%   y = dependent variable
+%   xx = value of independent variable at which
+%        interpolation is calculated
+% output:
+%   yint = interpolated value of dependent variable
+
+% compute the finite divided differences in the form of a
+% difference table
+n = length(x);
+if length(y)~=n, error('x and y must be same length'); end
+b = zeros(n,n);
+% assign dependent variables to the first column of b.
+b(:,1) = y(:); % the (:) ensures that y is a column vector.
+for j = 2:n
+  for i = 1:n-j+1
+    b(i,j) = (b(i+1,j-1)-b(i,j-1))/(x(i+j-1)-x(i));
+  end
+end
+%b
+% use the finite divided differences to interpolate
+xt = 1;
+yint = b(1,1);
+for j = 1:n-1
+  xt = xt*(xx-x(j));
+  yint = yint+b(1,j+1)*xt;
+end