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 (non structured) 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 LQN unconstrained optimization methods, which define Hessian approximations by updating nxn matrices from an algebra L, can be implemented for L=Ht with an O(n) amount of memory allocations and O(nlog_2 n) arithmetic operations per step. The LQN methods with the lowest experimental rate of convergence are shown to be linearly convergent.
DI FIORE, C., Lepore, F., Zellini, P. (2003). Hartley-type algebras in displacement and optimization strategies. LINEAR ALGEBRA AND ITS APPLICATIONS, 366, 215-232 [10.1016/S0024-3795(02)00499-8].
Hartley-type algebras in displacement and optimization strategies
DI FIORE, CARMINE;ZELLINI, PAOLO
2003-01-01
Abstract
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 (non structured) 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 LQN unconstrained optimization methods, which define Hessian approximations by updating nxn matrices from an algebra L, can be implemented for L=Ht with an O(n) amount of memory allocations and O(nlog_2 n) arithmetic operations per step. The LQN methods with the lowest experimental rate of convergence are shown to be linearly convergent.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
