The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of nonlinear equations systems through the N...

We are concerned with fast methods for the numerical implementation of the direct and inverse scattering problems for a perfectly conducting obstacle. The scattering problem is usually reduced to a single uniquely solvable modified combined-field integral equation (MCFIE). For the numerical solution of the M-CFIE we propose a new high-order spectral algorithm by transporting this equation on th...

A parallel fully coupled one-level Newton-Krylov-Schwarz method is investigated for solving the nonlinear system of algebraic equations arising from the finite difference discretization of inverse elliptic problems. Both L and H least squares formulations are considered with the H regularization. We show numerically that the preconditioned iterative method is optimally scalable with respect to ...

We introduce a partial proximal point algorithm for solving nuclear norm regularized matrix least squares problems with equality and inequality constraints. The inner subproblems, reformulated as a system of semismooth equations, are solved by an inexact smoothing Newton method, which is proved to be quadratically convergent under a constraint non-degeneracy condition, together with the strong ...

An analysis of two LMS-Newton adaptive filtering algorithms with variable convergence factor is presented. The relations of these algorithms with the conventional recursive least-squares algorithm are first addressed. Their performance in stationary and nonstationary environments is then studied and closed-form formulas for the excess mean-square error (MSE) are derived. The paper deals, in add...

In this notes we describe an algorithm for non-linear fitting which incorporates some of the features of linear least squares into a general minimum χ fit and provide a pure Python implementation of the algorithm. It consists of the variable projection method (varpro), combined with a Newton optimizer and stabilized using the steepest descent with an adaptative step. The algorithm includes a te...

In this work, a method for estimating the space-dependent perfusion coefficient parameter in a 2D bioheat transfer model is presented. In the method, the bioheat transfer model is transformed into a time-dependent semidiscrete system of ordinary differential equations involving perfusion coefficient values as parameters, and the estimation problem is solved through a nonlinear least squares tec...

This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics covered include: the choice of cost function and robustness; numerical optimization including spar...

The convergence performance of typical numerical schemes for geometric fitting for computer vision applications is compared. First, the problem and the associated KCR lower bound are stated. Then, three well known fitting algorithms are described: FNS, HEIV, and renormalization. To these, we add a special variant of Gauss-Newton iterations. For initialization of iterations, random choice, least...

Three novel adaptive multichannel L-filters based on marginal data ordering are proposed. They rely on well-known algorithms for the unconstrained minimization of the Mean Squared Error (MSE), namely, the Least Mean Squares (LMS), the normalized LMS (NLMS) and the LMS-Newton (LMSN) algorithm. Performance comparisons in color image filtering have been made both in RGB and U∗V ∗W ∗ color spaces. ...