相关论文: The logarithmic least squares priorities and ordin…
We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error…
Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise…
Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…
The least squares method provides the best-fit curve by minimizing the total squares error. In this work, we provide the modified least squares method based on the fractional orthogonal polynomials that belong to the space $M_{n}^{\lambda}…
Optimising queries in real-world situations under imperfect conditions is still a problem that has not been fully solved. We consider finding the optimal order in which to execute a given set of selection operators under partial ignorance…
Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are…
It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of…
We consider a setting in which it is desired to find an optimal complex vector $\mathbf{x}\in\mathbb{C}^N$ that satisfies $\mathcal{A}(\mathbf{x}) \approx \mathbf{b}$ in a least-squares sense, where $\mathbf{b} \in \mathbb{C}^M$ is a data…
A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph.…
Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must…
This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…
We study the performance of first- and second-order optimization methods for l1-regularized sparse least-squares problems as the conditioning of the problem changes and the dimensions of the problem increase up to one trillion. A rigorously…
A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…
We propose a linear algorithm for determining two function parameters by their linear combination. These functions must satisfy the first order differential equations with polynomial coefficients and our parameters are the coefficients of…
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…
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…