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From: Olta Çakaj on 1 Apr 2010 11:21
Do anyone know how to obtain ORES algorithm (Orthogonal Residual Method) starting from CG algorithm (Conjugate Gradients)?

ORES:
x0 ∈ C^N , r_0 = b − Ax_0
ρ(0)=||r(0)||, q(1) = r(0)/ρ(0), β(0) = 0, q(0) = 0
f or i = 1, 2, 3, . . .
v = Aq(i)
a(i) = q(i)^* v
v = v − q(i) a(i) − q(i-1) β(i-1)
β(i) = ||v||2
q(i+1) = v/β(i)
y(i) = T(i)\(ρ(0) e(1)) % T_i is a square matrix
x(i) = x(0) + Q(i) y(i)

CG:
v0=0, x0 ∈ C^N, t0=b-Ax0, p0=0
for i=1,2,3.....
p(i)=t(i-1)+v(i-1)p(i-1)
m(i)=(t(i-1),t(i-1))/((p(i),Ap(i))
x(i)=x(i-1)+m(i)p(i)
t(i)=t(i-1)-m(i)Ap(i)
v(i)=(t(i),t(i))/(t(i-1),t(i-1))
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