The Least Squares Hermitian (Anti)reflexive Solution with the Least Norm to Matrix Equation AXB=C

The least-square bisymmetric solution to a quaternion matrix equation with applications

In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. Futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. As applications, we derive sufficient and necess...

Global least squares solution of matrix equation $sum_{j=1}^s A_jX_jB_j = E$

In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...

Least squares solution with the minimum-norm to general matrix equations via iteration

L1-norm Penalized Least Squares with Salsa

This lecture note describes an iterative optimization algorithm, ‘SALSA’, for solving L1-norm penalized least squares problems. We describe the use of SALSA for sparse signal representation and approximation, especially with overcomplete Parseval transforms. We also illustrate the use of SALSA to perform basis pursuit (BP), basis pursuit denoising (BPD), and morphological component analysis (MC...

A Least Squares Approach to Estimating the Average Reservoir Pressure

Least squares method (LSM) is an accurate and rapid method for solving some analytical and numerical problems. This method can be used to estimate the average reservoir pressure in well test analysis. In fact, it may be employed to estimate parameters such as permeability (k) and pore volume (Vp). Regarding this point, buildup, drawdown, late transient test data, modified Muskat method, interfe...