CG -- Gram-Schmidt Conjugation


To construct a set of A-orthogonal search directions d(i).

High-level idea

Use n linearly independent vectors u0,u1,...,un1. To construct d(i), take ui and subtract out any components that are not A-orthogonal to the previous d vectors. In other words, set d(0)=u0, and for i>0, set


Find βik

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The difficulty with using Gram-Schmidt conjugation in the method of Conjugate Directions is that all the old search vectors must be kept in memory to construct each new one, and furthermore O(n3) operations are required to generate the full set.