# irls: Iteratively reweight least squares In PEIP: Geophysical Inverse Theory and Optimization

## Description

Uses the iteratively reweight least squares strategy to find an approximate L_p solution to Ax=b.

## Usage

 1 irls(A, b, tolr, tolx, p, maxiter)

## Arguments

 A Matrix of the system of equations. b Right hand side of the system of equations tolr Tolerance below which residuals are ignored tolx Stopping tolerance. Stop when (norm(newx-x)/(1+norm(x)) < tolx) p Specifies which p-norm to use (most often, p=1.) maxiter Limit on number of iterations of IRLS

## Details

Use to get L-1 norm solution of inverse problems.

## Value

 x Approximate L_p solution

## Author(s)

Jonathan M. Lees<[email protected]>

## References

Aster, R.C., C.H. Thurber, and B. Borchers, Parameter Estimation and Inverse Problems, Elsevier Academic Press, Amsterdam, 2005.

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 t = 1:10 y=c(109.3827,187.5385,267.5319,331.8753,386.0535, 428.4271,452.1644,498.1461,512.3499,512.9753) sigma = rep(8, length(y)) N=length(t); ### % Introduce the outlier y[4]=y[4]-200; G = cbind( rep(1, N), t, -1/2*t^2 ) ### % Apply the weighting yw = y/sigma; Gw = G/sigma m2 = solve( t(Gw) %*% Gw , t(Gw) %*% yw, tol=1e-12 ) ### Solve for the 1-norm solution m1 = irls(Gw,yw,1.0e-5,1.0e-5,1,25) m1

PEIP documentation built on Jan. 20, 2018, 9:03 a.m.