Developing suitable interpolation methods to simulate dynamic motions of continuous materials such as fluids is an important problem. In this paper, we propose a novel method to enforce the divergence condition to the interpolated velocity field by moving least squares, by means of the diffusive derivatives and moving divergence constraints that allow the practical use and easy implementation. ...

We derive an upper bound on the normwise backward error of an approximate solution to the equality constrained least squares problem minBx=d ‖b − Ax‖2. Instead of minimizing over the four perturbations to A, b, B and d, we fix those to B and d and minimize over the remaining two; we obtain an explicit solution of this simplified minimization problem. Our experiments show that backward error bou...

The problem of solving approximately in the least squares sense an overdetermined linear system of equations with complex valued coefficients is considered, where the elements of the solution vector are constrained to have the same phase. A direct solution to this problem is given in [Linear Algebra and Its Applications, Vol. 433, pp. 1719–1721]. An alternative direct solution that reduces the ...

We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide the first theoretical convergence analysis for both algorithms. An efficient implementation using a tailored linesearch scheme is also proposed. We demonstrate our methods’ computational e...

We present theory and algorithms for the equality constrained indefinite least squares problem, which requires minimization of an indefinite quadratic form subject to a linear equality constraint. A generalized hyperbolic QR factorization is introduced and used in the derivation of perturbation bounds and to construct a numerical method. An alternative method is obtained by employing a generali...

In this chapter a randomized ellipsoid algorithm is described that can be used for finding solutions to robust Linear Matrix Inequality (LMI) problems. The iterative algorithm enjoys the property that the convergence speed is independent on the number of uncertain parameters. Other advantages, as compared to the deterministic algorithms, are that the uncertain parameters can enter the LMIs in a...

Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation. We show that a simple sign-constrained least squares estimation is a very simple and effective regularization technique for a certain class of high-dimensional regression problems. The sign constraint has to be deri...

1 The paper proposes a Constrained Least Square (CLS) pre-distortion scheme for multiple-input 2 single-output (MISO) multiple access ultra-wideband (UWB) systems. In such a scheme, a simple 3 objective function is defined, which can be efficiently solved by a gradient based algorithm. For the 4 performance evaluation, scenarios CM1 and CM3 of the IEEE 802.15.3a channel model are considered. 5 ...

Performance analysis of l0 norm constrained Recursive least Squares (RLS) algorithm is attempted in this paper. Though the performance pretty attractive compared to its various alternatives, no thorough study of theoretical analysis has been performed. Like the popular l0 Least Mean Squares (LMS) algorithm, in l0 RLS, a l0 norm penalty is added to provide zero tap attractions on the instantaneo...

In this work we present an iterative algorithm for solving a parameter identification problem relative to a system of diffusion, convection and reaction equations. The parameters to estimate are the retardation factors, diffusivity, reaction and transport coefficients relative to a model of pollutant transport with chemical reaction. The proposed method solves the nonlinear least squares proble...