On Duality and the Bi-Conjugate Gradient Algorithm

It is not uncommon to encounter problems that lead to large, sparse linear systems with coefficient matrices that are invertible and sparse, but have little other structure. In such problems the solution u=A¹ƒ is typically calculated only to acurately compute functionals of the solution, L(u). This paper determines a method that converges rapidly to the functional's value. Specifially, a modified bi-conjugate gradient algorithm is found to generate convergence to the solution of linear functionals, L(u), much more rapidly than convergence to the linear system solution u