kac: Kaczmarz

In PEIP: Geophysical Inverse Theory and Optimization

Kaczmarz

Description

Implements Kaczmarz's algorithm to solve a system of equations iteratively

Usage

kac(A, b, tolx, maxiter)

Arguments

A	Constraint matrix
b	right hand side
tolx	difference tolerence for successive iterations (stopping criteria)
maxiter	maximum iterations (stopping criteria)

Value

x

solution

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(2015)
G = setDesignG()
### % Setup the true model.
mtruem=matrix(rep(0, 16*16), ncol=16,nrow=16);

mtruem[9,9]=1; mtruem[9,10]=1; mtruem[9,11]=1;
mtruem[10,9]=1; mtruem[10,11]=1;
mtruem[11,9]=1; mtruem[11,10]=1; mtruem[11,11]=1;
mtruem[2,3]=1; mtruem[2,4]=1;
mtruem[3,3]=1; mtruem[3,4]=1;

### % reshape the true model to be a vector
mtruev=as.vector(mtruem);

### % Compute the data.
dtrue=G %*% mtruev;

### % Add the noise.

d=dtrue+0.1*rnorm(length(dtrue));

mkac<-kac(G,d,0.0,200)
par(mfrow=c(1,2))
imagesc(matrix(mtruem,16,16) , asp=1 , main="True Model" );

imagesc(matrix(mkac,16,16) , asp=1 , main="Kacz Solution" );

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