A new algorithm for constrained matrix least squares approximations

This paper considers the problem of approximating a given symmetric matrix by a symmetric matrix with a prescribed spectrum so that the Frobenius norm of the matrix difference is minimized. By the introduction of a variable search direction, a new convergent algorithm for solving the problem is derived, which is guaranteed to be convergent and is capable of achieving a fast rate of convergence. It is shown that the set of fixed points of the proposed algorithm coincides with the set of equilibrium points of the original double bracket equation. A numerical example is presented to demonstrate superior performance of the proposed algorithm over a standard double bracket algorithm.