Recent attention to the problem of controlling multiple loudspeakers to create sound zones has been directed towards practical issues arising from system robustness concerns. In this study, the effects of regularization are analyzed for three representative sound zoning methods. Regularization governs the control effort required to drive the loudspeaker array, via a constraint in each optimizat...

The solution, x, of the linear system of equations Ax ≈ b arising from the discretization of an ill-posed integral equation g(s) = ∫ H(s, t)f(t) dt with a square integrable kernel H(s, t) is considered. The Tikhonov regularized solution x(λ) approximating the Galerkin coefficients of f(t) is found as the minimizer of J(x) = {‖Ax− b‖2 +λ‖Lx‖2}, where b is given by the Galerkin coefficients of g(...

We consider a local regularization method for the solution of first-kind Volterra integral equations with convolution kernel. The local regularization is based on a splitting of the original Volterra operator into “local” and “global” parts, and a use of Tikhonov regularization to stabilize the inversion of the local operator only. The regularization parameters for the local procedure include t...

A popular approach to recover low rank matrices is the nuclear norm regularized minimization (NRM) for which selection of regularization parameter inevitable. In this paper, we build up a novel rule choose NRM, with help duality theory. Our result provides safe set when solution has an upper bound. Furthermore, apply idea NRM quadratic and Huber functions, establish simple formulae parameters. ...