Changes between Version 15 and Version 16 of PolynomialExpansion

Timestamp:

01/26/16 12:52:10 (10 years ago)

Author:

sili

Comment:

--

PolynomialExpansion

@@ -9 +9 @@
 
 Step 2: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])
+  p[i]*(A[i][j]*p[j]) = X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^
+
   alpha = (X3[0]^2^+X3[1]^2^) / ((X3[1]^2^)*X2+2*(X3[1]*X3[0]*X1)+(X3[0]^2^)*X0)
 
@@ -21 +23 @@
   x[1] = (X3[1]*(X3[0]^2^ + X3[1]^2^)) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)
 
-Step 5: beta = (rk[i]*rk[i]) / (r[i]*r[i])
+Step 5: beta = rsnew / rsold = (rk[i]*rk[i]) / (r[i]*r[i])
+  rsnew = ((X3[0]^2^ + X3[1]^2^)*(-X1*X3[0]^2^ + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2^)^2^) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)^2^
+
   beta = (X1*X3[0]^2^ - X0*X3[0]*X3[1] + X2*X3[0]*X3[1] - X1*X3[1]^2^)^2^ / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)^2^
 
@@ -30 +34 @@
 
 Step 7: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])
+  p[i]*(A[i][j]*p[j]) = ((-X1^2^ + X0*X2)*(X3[0]^2^ + X3[1]^2^)^2^*(-X1*X3[0]^2^ + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2^)^2^) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)^3^
+
   alpha = (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^) / ((-X1^2^ + X0*X2) (X3[0]^2^ + X3[1]^2^))