相关论文: Least Sqaure Method for Sum of the Functions Satys…

Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Network (LS-Net) method for solving linear parametric PDEs. It…

This paper shows how to obtain highly accurate solutions of eighth-order boundary-value problems of linear and nonlinear ordinary differential equations. The presented method is based on the Theory of Functional Connections, and is solved…

This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multi-agent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than…

The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper,…

We propose an algorithm for reduction of the problem of maximization of fraction of two functionals to the equivalent procedure including maximization of difference between the functionals and the solution of an equation of scalar unknown.…

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…

In this article, we present a method for increasing adaptivity of an existing robust estimation algorithm by learning two parameters to better fit the residual distribution. The analyzed method uses these two parameters to calculate weights…

We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…

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…

This paper discusses how to find the global minimum of functions that are summations of small polynomials (``small'' means involving a small number of variables). Some sparse sum of squares (SOS) techniques are proposed. We compare their…

We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…

We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…

Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas,…

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…

We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs…

A distributed discrete-time algorithm is proposed for multi-agent networks to achieve a common least squares solution of a group of linear equations, in which each agent only knows some of the equations and is only able to receive…

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…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the…

This paper presents a canonical dual approach to the problem of minimizing the sum of a quadratic function and the ratio of nonconvex function and quadratic functions, which is a type of non-convex optimization problem subject to an…