The Stability Of Interior-Point Algorithms

A new stable algorithm to compute the projection P-WA =(WA)(WA)(+) when W is a stiff matrix is given, and is applied to compute the Newton direction (Delta x, Delta y, Delta z) in interior-point algorithms for linear programming. Numerical experiments show that this algorithm can keep high precision even the scaling matrix D-k is badly scaled in last iterates in interior-point algorithms.