LSregression

Introduction

• Implementing Gauss-Newton with different conjugate gradient methods, including

  • without conjugate gradient

  • standard conjugate gradient

  • preconditioned conjugate gradient

  • CG-Steihaug

  • preconditioned CG-Steihaug

• Implementing Levenberg-Marquardt with some methods to increase speed and robustness

  • damping strategy of lambda, due to Nielsen:

    • Methods for nonlinear least squares problems - introduction and comparison

    • Damping Parameter in Marquardt's Method - original & statistic detail

  • CG-Steihaug

  • preconditioning

Getting Start

Carrying out data-fitting test: nonlinear_datafitting_test.m

Nonlinear Least-Squares solver: pcg_steihaug_gauss_newton.m

ClassDef

Example cases saved in data folder

• dim_1_case: f_i(x) = exp(d_i*x)

• dim_2_case.m: f_i(x) = exp( d_i * x_1 ) * sin( d_i * x_2 )

• dim_2_quadratic_case.m: f_i(x) = d_i * x_1 + d_i.^2 * x_2