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diff --git a/Lagrange_interpolation.m b/Lagrange_interpolation.m
index e53a21995af603048408df4b62769964ad1f008d..34b6f0552cfb00007186aacc9fa40ff03ce388ac 100644 (file)
--- a/Lagrange_interpolation.m
+++ b/Lagrange_interpolation.m
@@ -1,4 +1,4 @@
-function [pnx] = Lagrange_interpolation(z,)
+function [pnx] = Lagrange_interpolation(z,x,y)
 %%
 %  Implementation to evaluate an interpolating polynomial p_n(x) 
 %  at the point x = z. The polynomial uses the standard Lagrange
@@ -7,8 +7,8 @@ function [pnx] = Lagrange_interpolation(z,)
 %  INPUT:
 %
 %     z    - 1x1 value to evaluate
-%     ???
-%
+%     x    - nx1 vector with x-values
+%     y    - nx1 vector with y-valuse
 %  OUTPUT:
 %
 %     pnx - value of the polynomial interpolant at x = z
@@ -16,17 +16,17 @@ function [pnx] = Lagrange_interpolation(z,)
 
 %%
 %  compute the polynomial interpolation sum evaluated at x = z
-   pnx =
-   for i =
-
-
-
-      for j =
-
-
-
+   pnx = 0;
+   n = length(x);
+   l = ones(n,1);
+   for i=1:n
+
+      for j=1:n
+        if i ~= j
+            l(i) = l(i)*(z - x(j))/(x(i) - x(j));
+        end
       end
-
-      pnx =
+              l(i)
+      pnx = pnx + (y(i) * l(i));
    end
 end

diff --git a/build_interpolation.m b/build_interpolation.m
new file mode 100644 (file)
index 0000000..7f2e318
--- /dev/null
+++ b/build_interpolation.m
@@ -0,0 +1,9 @@
+function [X,L] = build_interpolation(M, xVals, yVals)
+%UNTITLED Summary of this function goes here
+%   Detailed explanation goes here
+    X = linspace(xVals(1), xVals(end), M);
+    L = zeros(length(M), 1);
+    for k=1:M
+        L(k) = Lagrange_interpolation(X(k), xVals, yVals);
+    end
+end
\ No newline at end of file

diff --git a/command_windwo todat.mat b/command_windwo todat.mat
new file mode 100644 (file)
index 0000000..b423bd1
Binary files /dev/null and b/command_windwo todat.mat differ

diff --git a/diff.m b/diff.m
index 64e8bf7dbac9fdd267728622b88abb3b85ad59de..ba02172ec752344819bb1b6008864845d8d83c12 100644 (file)
--- a/diff.m
+++ b/diff.m
@@ -57,7 +57,7 @@ bound_up = ((f_x_3(4)) - (4*f_x_3(5)) + (3*f_x_3(6)))/(2*h)
 
 
 %% EXP
-N = 100;
+N = 1000;
 
 D_x_center = diag(0.5*ones(N,1),1) - diag(0.5*ones(N,1),-1);
 D_x_center(1,1) = 1;
@@ -72,16 +72,24 @@ h = 1/N;
 f = zeros(length(interval), 1);
 f_prim = zeros(length(interval), 1);
 for i=1:length(interval)
-    f(i) = 4*exp(sin(4*interval(i)));
+    f(i) = exp(sin(4*interval(i)));
     f_prim(i) = 4*exp(sin(4*interval(i)))*cos(4*interval(i));
 end
 
-D_x_center
-interval
-f
 
-approx = (1/h) * D_x_center * f
-f_prim
+approx_mid = (1/h) * D_x_center * f;
+%approx_edge = (1/h) * D_x_forward * f;
+%approx_mid(1) = approx_edge(1);
+%approx_mid(end) = approx_edge(end);
+
+bound_low = ((-3*f(1)) + (4*f(2)) - (f(3)))/(2*h);
+bound_up = ((f(N-2)) - (4*f(N-1)) + (3*f(N)))/(2*h);
+
+approx_mid(1) = bound_low;
+approx_mid(end) = bound_up;
+
+max(abs(f_prim - approx_mid))
+
 
 
 

diff --git a/scripting.m b/scripting.m
new file mode 100644 (file)
index 0000000..0897810
--- /dev/null
+++ b/scripting.m
@@ -0,0 +1,21 @@
+xVals = [1, 2, 3, 4, 5];
+yVals = [1, 1, 2, 6, 24];
+[X, L] = build_interpolation(150, xVals, yVals);
+%plot(X, gamma(X), '-k' , X, L, '--r', xVals, yVals, 'rd', 'MarkerFaceColor', 'r', 'MarkerSize', 7)
+
+p = Lagrange_interpolation(6, xVals, yVals)
+q = gamma(6)
+sqrt(pi)/2
+
+%%
+
+xVals = x_joukow;
+yVals = y_joukow;
+[X, L] = build_interpolation(150, xVals, yVals);
+
+M = linspace(-1.775, 1.695, 150);
+s = spline(x_joukow, y_joukow, M);
+
+
+plot(X, L, '--r', xVals, yVals, 'rd', 'MarkerFaceColor', 'r', 'MarkerSize', 7)
+plot(M, s, '-.g', 'LineWidth', 2);
\ No newline at end of file