Linear inequalities via least squares

Self-Calibration via Linear Least Squares

Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive and sometimes even impossible to implement. We study a challenging problem called self-calibration, i.e., the task of designing an algorithm for devices so that the algorithm is able to perform ca...

Solving Linear Inequalities in a Least Squares Sense

In 1980, Han 5] described a nitely terminating algorithm for solving a system Ax b of linear inequalities in a least squares sense. The algorithm requires a singular value decomposition of a submatrix of A on each iteration, making it impractical for all but the smallest problems. This paper shows that a modiication of Han's algorithm allows the iterates to be computed using QR factorization wi...

Linear Least Squares Problems

A fundamental task in scientific computing is to estimate parameters in a mathematical model from collected data which are subject to errors. The influence of the errors can be reduced by using a greater number of data than the number of unknowns. If the model is linear, the resulting problem is then to “solve” an in general inconsistent linear system Ax = b, where A ∈ Rm×n and m ≥ n. In other ...

Non-linear Least Squares

Using measured radial velocity data of nine double lined spectroscopic binary systems NSV 223, AB And, V2082 Cyg, HS Her, V918 Her, BV Dra, BW Dra, V2357 Oph, and YZ Cas, we find corresponding orbital and spectroscopic elements via the method introduced by Karami & Mohebi (2007a) and Karami & Teimoorinia (2007). Our numerical results are in good agreement with those obtained by others using mor...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations