Stability of Two Direct Methods for Bidiagonalization and Partial Least Squares

Partial least-squares vs. Lanczos bidiagonalization - I: analysis of a projection method for multiple regression

Tikhonov Regularization with a Solution Constraint

Many numerical methods for the solution of linear ill-posed problems apply Tikhonov regularization. This paper presents a modification of a numerical method proposed by Golub and von Matt for quadratically constrained least-squares problems and applies it to Tikhonov regularization of large-scale linear discrete ill-posed problems. The method is based on partial Lanczos bidiagonalization and Ga...

Inexact trust region method for large sparse nonlinear least squares

The main purpose of this paper is to show that linear least squares methods based on bidiagonalization, namely the LSQR algorithm, can be used for generation of trust region path. This property is a basis for an inexact trust region method which uses the LSQR algorithm for direction determination. This method is very efficient for large sparse nonlinear least squares as it is supported by numer...

Partial least squares- least squares- support vector machine modeling of ATR-IR as a spectrophotometric method for detection and determination of iron in pharmaceutical formulations

Iron is an essential element used as supplement in different dosage-forms. Different time and expenditure-consuming methods introduced for detection and determination of elemental ions such as atomic absorption. In this research, two different and routine methods containing ATR-IR and atomic absorption were applied to define the amount of iron in 198 samples containing different concentrations ...

Rapid and Simultaneous Determination of Montelukast, Fexofenadine and Cetirizine Using Partial Least Squares and Artificial Neural Networks Modeling

Simultaneous determination of pharmaceutical compounds and accurate quantitative prediction of them are of great interest in the clinical and laboratory-based investigations.This work has focused on a comprehensive comparison of Partial Least-Squares (PLS-1) and Artificial Neural Networks (ANN) as two powerful types of chemometric methods. For this purpose, montelukast (MONT), fexofenadine ...