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Conjugate gradient method of Golub and van Loan

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Conjugate gradient method

Conjugate gradient method could be summarized as follows

System of equation

For the given system of equation
Ax = b ;
b = source vector
x = solution variable for which we seek the solution
A = coefficient matrix

M = the precondioning matrix constructued by matrix A


 Allocate temperary vectors p,z,q 
Allocate temerary reals rho_0, rho_1 , alpha, beta
r := b - A\bulletx
for i := 1 step 1 until max_itr do solve (M\bulletz = r )
beta := rho_0 / rho_1
p := z + beta\bulletp
q := A\bulletp
alpha = rho_0 / ( p\bulletq )
x := x + alpha\bulletp
r := r - alpha\bulletq
rho_1 = rho_0
end (i-loop) deallocate all temp memory
return TRUE


Ferziger, J.H. and Peric, M. 2002. "Computational Methods for Fluid Dynamics", 3rd rev. ed., Springer-Verlag, Berlin.

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