Conditions for Termination of the Method of Steepest Descent after a Finite Number of Iterations

Certain problems in mathematical physics can be recast as extremum problems of quadratic functionals. In particular, considerable attention has been givent o them inimization of a quadratic polynomial associated with a bounded and positive semidefinite linear operator T defined on a Hilbert space H, viz., the quadratic polynomial Q(x) = [Tx,x ] − [x, g] − [g, x]w, here g is a fixed element of H and [,] denotes dot product.