thomas tridiagonal and spectral radius

samples/sample_matrices.m

@@ -1 +1,5 @@
+%band 2 2
 A=[6,-1,-1,0,0,0,0,0,0;-1,6,-1,-2,0,0,0,0,0;-3,-1,6,0,-1,0,0,0,0;0,-1,0,6,-1,-1,0,0,0;0,0,-1,-1,6,-1,-1,0,0;0,0,0,-3,-1,6,0,-1,0;0,0,0,0,-1,0,6,-1,-2;0,0,0,0,0,-1,-1,6,-1;0,0,0,0,0,0,-1,-1,6]
+
+%tridiagonal
+A = [5,1,0,0;4,5,1,0;0,1,3,5;0,0,4,6]

samples/spettro.m

@@ -0,0 +1,39 @@
+%Ax=b
+%A = X + Y
+
+%x = inv(X) *b - (inv(X) * Y *x)
+
+% se C = inv(X) * b    e     B = -(inv(X) * Y )
+% allora x = Bx + C
+
+%metodo iterativo converge se e solo se il raggio spettrale di B < 1
+% raggio spettrale = max (abs(eig(B)))
+
+
+%in jacobi X = diag(diag(A))  e Y = A - X
+%in gauss-seidel X = tril(A)  e Y = A - X
+
+
+
+%quindi
+
+%jacobi B =  -(inv(diag(diag(A))) * (A - (diag(diag(A)))) )
+%jacobi C =  inv(diag(diag(A))) * b
+
+%gauss B =  -(inv(tril(A)) * (A - (tril(A))) )
+%gauss C =  inv(tril(A)) * b 
+
+
+%formula definitiva
+%jacobi converge se
+% max(abs(eig((-(inv(diag(diag(A))) * (A - (diag(diag(A)))) )))))
+% <1
+
+%gauss converge se
+% max(abs(eig(-(inv(tril(A)) * (A - (tril(A))) ))))
+% <1
+
+
+
+
+