Performance Analysis of Steepest Descent-Line Search Condition Combinations in Nonlinear Least Squares Fitting of CMM Data

Least Squares Fitting of Data

This is the usual introduction to least squares fit by a line when the data represents measurements where the y–component is assumed to be functionally dependent on the x–component. Given a set of samples {(xi, yi)}i=1, determine A and B so that the line y = Ax + B best fits the samples in the sense that the sum of the squared errors between the yi and the line values Axi + B is minimized. Note...

SVM-Optimization and Steepest-Descent Line Search

We consider (a subclass of) convex quadratic optimization problems and analyze decomposition algorithms that perform, at least approximately, steepest-descent exact line search. We show that these algorithms, when implemented properly, are within ǫ of optimality after O(log 1/ǫ) iterations for strictly convex cost functions, and after O(1/ǫ) iterations in the general case. Our analysis is gener...

A Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems

In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...

Least-Squares Fitting of Data with Polynomials

PEDOMODELS FITTING WITH FUZZY LEAST SQUARES REGRESSION

Pedomodels have become a popular topic in soil science and environmentalresearch. They are predictive functions of certain soil properties based on other easily orcheaply measured properties. The common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. In modeling natural systems such as s...