Related papers: Moving least squares via orthogonal polynomials
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…
We introduce a new fundamental algorithm called Matrix-POAFD to solve the matrix least square problem. The method is based on the matching pursuit principle. The method directly extracts, among the given features as column vectors of the…
The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge…
This paper presents a new approach to the detection of discontinuities in the n-th derivative of observational data. This is achieved by performing two polynomial approximations at each interstitial point. The polynomials are coupled by…
We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular…
In the paper we consider the problem of multivariate function approximation in polynomial basis. In order to solve this problem, we adjust the least squares method (LSM) by adding information about derivatives of the function. This…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
Orthogonal polynomials in two variables on cubic curves are considered, including the case of elliptic curves. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal…
The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting…
Let $d\nu$ be a measure in $\mathbb{R}^d$ obtained from adding a set of mass points to another measure $d\mu$. Orthogonal polynomials in several variables associated with $d\nu$ can be explicitly expressed in terms of orthogonal polynomials…
In this paper we are concerned with numerical methods for nonhomogeneous Helmholtz equations in inhomogeneous media. We design a least squares method for discretization of the considered Helmholtz equations. In this method, an auxiliary…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
This paper is concerned with Lagrange interpolation by total degree polynomials in moderate dimensions. In particular, we are interested in characterising the optimal choice of points for the interpolation problem, where we define the…
Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…
We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…
A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual equally important, the new procedure exponentially…
We describe a generalised method for ellipsoid fitting against a minimum set of data points. The proposed method is numerically stable and applies to a wide range of ellipsoidal shapes, including highly elongated and arbitrarily oriented…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
In this note we discuss several questions concerning the implementation of overdetermined least-squares collocation methods for higher-index differential algebraic equations (DAEs). Since higher-index DAEs lead to ill-posed problems in…