ISSN:
1070-5325
Keywords:
alternating projection method
;
Dykstra's algorithm
;
patterned matrix
;
constrained least-squares
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
We apply Dykstra's alternating projection algorithm to the constrained least-squares matrix problem that arises naturally in statistics and mathematical economics. In particular, we are concerned with the problem of finding the closest symmetric positive definite bounded and patterned matrix, in the Frobenius norm, to a given matrix. In this work, we state the problem as the minimization of a convex function over the intersection of a finite collection of closed and convex sets in the vector space of square matrices.We present iterative schemes that exploit the geometry of the problem, and for which we establish convergence to the unique solution. Finally, we present preliminary numberical results to illustrate the performance of the proposed iterative methods.
Additional Material:
4 Tab.
Type of Medium:
Electronic Resource
