Related papers: Polynomial least squares fitting in the Bernstein …
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…
We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…
Randomized neural networks (RaNNs), in which hidden layers remain fixed after random initialization, provide an efficient alternative for parameter optimization compared to fully parameterized networks. In this paper, RaNNs are integrated…
Model reduction using the proper orthogonal decomposition (POD) method is applied to the dynamics of ferroelastic patches to study the first order square to rectangular phase transformations. Governing equations for the system dynamics are…
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…
Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…
We introduce a randomized algorithm for computing the minimal-norm solution to an underdetermined system of linear equations. Given an arbitrary full-rank m x n matrix A with m<n, any m x 1 vector b, and any positive real number epsilon…
The Total Least Squares solution of an overdetermined, approximate linear equation $Ax \approx b$ minimizes a nonlinear function which characterizes the backward error. We show that a globally convergent variant of the Gauss--Newton…
The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute…
Given a polynomial $x \in {\mathbb R}^n \mapsto p(x)$ in $n=2$ variables, a symbolic-numerical algorithm is first described for detecting whether the connected component of the plane sublevel set ${\mathcal P} = \{x : p(x) \geq 0\}$…
Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements…
To find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the error term, such that a consistent system is asymptotically…
We study the least-squares (LS) functional of the canonical polyadic (CP) tensor decomposition. Our approach is based on the elimination of one factor matrix which results in a reduced functional. The reduced functional is reformulated into…
In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an inverse eigenvalue problem, which can be solved using…
A numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear…
In computer aided geometric design a polynomial is usually represented in Bernstein form. The de Casteljau algorithm is the most well-known algorithm for evaluating a polynomial in this form. Evaluation via the de Casteljau algorithm has…
This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds…
The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…
In this research, we solve polynomial, Sobolev polynomial, rational, and Sobolev rational least squares problems. Although the increase in the approximation degree allows us to fit the data better in attacking least squares problems, the…