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Methods for Least Squares Problems
In this chapter we consider least squares problems, which constitute an important class of unconstrained optimization problems. First we recall some...
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Least-Squares Estimation
Least-squares estimation provides a means of determining estimates of model parameters that are optimal in the sense of minimizing the sum of the...
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Least-squares finite elements for distributed optimal control problems
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our...
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Weighted Tensor Least Angle Regression for Solving Sparse Weighted Multilinear Least Squares Problems
Sparse weighted multilinear least-squares is a generalization of the sparse multilinear least-squares problem, where prior information about, e.g.,...
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Mixed precision Rayleigh quotient iteration for total least squares problems
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems...
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Least-Squares Virtual Element Method for Stokes Problems on Polygonal Meshes
In this paper, a least-squares virtual element method on polygonal meshes is proposed for the stress-velocity formulation of the linear Stokes...
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Average block column action methods for solving least squares problems
The column action methods of algebraic iterative techniques play a pivotal role in the image reconstruction process. These methods converge to a...
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A new structured spectral conjugate gradient method for nonlinear least squares problems
Least squares models appear frequently in many fields, such as data fitting, signal processing, machine learning, and especially artificial...
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On greedy randomized block Gauss–Seidel method with averaging for sparse linear least-squares problems
This paper presents a greedy randomized average block sampling Gauss–Seidel (GRABGS) method for solving sparse linear least-squares problems. The...
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Critical Points for Least-Squares Estimation of Dipolar Sources in Inverse Problems for Poisson Equation
In this work, we study some aspects of the solvability of the minimization of a non-convex least-squares criterion involved in dipolar source...
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A Comparative Study on Two Mixed Least Squares Meshless Models with Improved SPH, MPS and CPM Methods to Solve Elasticity Problems
This paper investigates the accuracy of several meshless methods to solve elasticity problems. The methods include the well-known smoothed particle...
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A least squares approach for saddle point problems
Saddle point linear systems arise in many applications in computational sciences and engineering such as finite element approximations to Stokes...
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Least Squares Optimization
The last chapter concluded with a nonlinear least squares formulation of the (full) SLAM problem and provided an intuitive analogy that helps to...
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A Semismooth Newton-based Augmented Lagrangian Algorithm for Density Matrix Least Squares Problems
The density matrix least squares problem arises from the quantum state tomography problem in experimental physics and has many applications in signal...
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On multi-step greedy randomized coordinate descent method for solving large linear least-squares problems
To solve large-scale linear least-squares problems, we propose a multi-step greedy randomized coordinate descent method based on the greedy...
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Estimating error norms in CG-like algorithms for least-squares and least-norm problems
In Meurant et al. (Numer. Algorithms 88 (3), 1337–1359,
2021 ), we presented an adaptive estimate for the energy norm of the error in the conjugate...
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Structured adaptive spectral-based algorithms for nonlinear least squares problems with robotic arm modelling applications
This research article develops two adaptive, efficient, structured non-linear least-squares algorithms, NLS. The approach taken to formulate these...
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Solving large linear least squares problems with linear equality constraints
We consider the problem of solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly....
