A = x0, x1 b = x3[2]

x1, x2

Step 1: r = b - Ax

r[0] = x3[0] r[1] = x3[1]

Step 2: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])

alpha = (X3[0]²+X3[1]²) / ((X3[1]²)*X2+2*(X3[1]*X3[0]*X1)+(X3[0]²)*X0)

Step 3: r[i] = r - alpha * A[i][j] * p[j]

r[0] = (-X3[1]*(-X1*X3[0]² + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]²)) / (X0*X3[0]² + 2*X1*X3[0]*X3[1] + X2*X3[1]²)

r[1] = (X3[0]*(-X1*X3[0]² + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]²)) / (X0*X3[0]² + 2*X1*X3[0]*X3[1] + X2*X3[1]²)

Step 4: x[i] = x + alpha*p[i]

x[0] = (X3[0]*(X3[0]^{2 + X3[1]}2)) / (X0*X3[0]^{2 + 2*X1*X3[0]*X3[1] + X2*X3[1]}2)

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])

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

Step 6: p[i] = rk[i] +beta * p

p[0] = (-1)*((X1*X3[0] + X2*X3[1])*(X3[0]^{2 + X3[1]}2)*(-X1*X3[0]^{2 + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]}2)) / (X0*X3[0]^{2 + 2*X1*X3[0]*X3[1] + X2*X3[1]}2)²

p[1] = ((X0*X3[0] + X1*X3[1])*(X3[0]^{2 + X3[1]}2)*(-X1*X3[0]^{2 + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]}2)) / (X0*X3[0]^{2 + 2*X1*X3[0]*X3[1] + X2*X3[1]}2)²

Step 7: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])

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⁾⁾

Step 8: r[i] = r - alpha * A[i][j] * p[j]

r[0] = 0 r[1] = 0

Step 9: x[i] = x + alpha*p[i]

x[0] = (X2*X3[0] - X1*X3[1]) / (X0*X2 - X1^{2) x[1] = (-X1 X3[0] + X0 X3[1]) / (X0*X2 - X1}2)

END