Hartley-type algebras in displacement and optimization strategies Original Research Article

The Hartley-type (Ht) algebras are used to face efficiently the solution of structured linear systems and to define low complexity methods for solving general (nonstructured) nonlinear problems. Displacement formulas for the inverse of a symmetric Toeplitz matrix in terms of Ht transforms are compared with the well known Ammar–Gader formula. The image unconstrained optimization methods, which define Hessian approximations by updating n×n matrices from an algebra image, can be implemented for image with an O(n) amount of memory allocations and O(nlogn) arithmetic operations per step. The image methods with the lowest experimental rate of convergence are shown to be linearly convergent.