Input: A , B , J , w ( 0 ) = [ z 1 ( 0 ) ; z 2 ( 0 ) ] , α ( 0 ) , β ( 0 ) , k m a x , tol

for k = 0 , 1 , 2 , until convergence do

Solve M ( k ) u ( k ) = B 1 w ( k ) inexactly using Algorithm 2.

Compute n α = w T B 1 J u and n β = w T B 1 u

Solve

[ n β n α n α n β ] [ Δ α Δ β ] = [ 1 2 ( w T B 1 w + 1 ) 0 ] , for [ Δ α Δ β ] .

Form the vector w + = Δ α u Δ β J u .

Update

[ α + β + ] = [ α β ] + [ Δ α Δ β ] .

end for

Output: v ( k m a x ) = [ w ( k m a x ) , α ( k m a x ) , β ( k m a x ) ] .