Brennan–Schwartz Algorithm Let A be a tridiagonal matrix as in (C1.6), and b and g vectors. The system of equations Aw = b is to be solved such that the side condition w ≥ g is obeyed componentwise. Assume for the case of a put wi = gi for 1 ≤ i ≤ if and wi > gi for if < i ≤ n, where if is unknown.

a) Formulate an algorithm similar as in (C1.7) that solves Aw = b in the backward/forward approach. In the final forward loop, for each i the calculated candidate ˜wi is tested for wi ≥ gi: Set wi := max{w˜i, gi} .

b) Apply the algorithm to the case of a put with A,

b, g from Section 4.6.1. For the case of a call adapt the forward/backward algorithm (C1.7). Incorporate this approach into Algorithm 4.13 by replacing the PSOR-loop.