cgls: Conjugate gradient Least squares

In PEIP: Geophysical Inverse Theory and Optimization

Conjugate gradient Least squares

Description

Conjugate gradient Least squares

Usage

cgls(Gmat, dee, niter)

Arguments

Gmat	input matrix
dee	right hand side
niter	max number of iterations

Details

Performs niter iterations of the CGLS algorithm on the least squares problem min norm(G*m-d). Gmat should be a sparse matrix.

Value

X	matrix of models
rho	misfit norms
eta	model norms

Author(s)

Jonathan M. Lees<[e-mail]>

References

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

Examples

set.seed(11)
####  perfect data with no noise
n <- 5
A <- matrix(runif(n*n),nrow=n)
B <- runif(n)
###  get right-hand-side (data)
trhs = as.vector( A %*% B  )
Lout = cgls(A, trhs , 15)

###  solution is
Lout$X[,15]

Lout$X[,15] - B

PEIP documentation built on Aug. 21, 2023, 9:10 a.m.