A fast algorithm for −1 factorization of Toeplitz matrices

Abstract

A fast algorithm foT solving large scale MV (mean-variance) portfolio optimization problems is proposed, It is shown that by using T independent data representing the rate of return of the assets, the MV model consisting of n assets can be put into a quadratic program with n + T variables, T linear constraints and T quadratic terms in the objective function. As a result, the computation t,ime required to solve this problem wou}d increase very mildly as a function of n. This implies that a very laJ:ge scale MV model can now be solved in a practical amount of time.

Fast Affine Projection Adaptation Algorithms With Stable and Robust Symmetric Linear System Slovers

“…Given SP.1, (21) may not need to be solved from scratch every sample; it can be done at a decimated rate of once every samples. If so, the average per-sample complexity figures for solving (13) Referring to (14), (27) indicates that, even at , the Ratchet approach offers a computational saving over the Levinson-Durbin's approach, whereas the two lead to virtually the same solution.…”

“…For clarity, we now introduce for a matrix or vector a subscript (13) with being symmetric and Toeplitz. To solve (13) with a general RHS, the well-known LevinsonDurbin's recursion [8] requires and (14) This is the approach [6] uses. Being a generalization of an approach proposed in [16] and adopted in [17], our proposal takes advantage of SP.3 to simplify the process.…”