sirt: SIRT Algorithm for sparse matrix inversion

In PEIP: Geophysical Inverse Theory and Optimization

SIRT Algorithm for sparse matrix inversion

Description

Row action method for inversion of matrices, using SIRT algorithm.

Usage

sirt(A, b, tolx, maxiter)

Arguments

A	Design Matrix
b	vector, Right hand side
tolx	numeric, tolerance for stopping
maxiter	integer, Maximum iterations

Details

Iterates until conversion

Value

Solution vector

Author(s)

Jonathan M. Lees<[e-mail]>

References

Lees, J. M. and R. S. Crosson (1989): Tomographic inversion for three-dimensional velocity structure at Mount St. Helens using earthquake data, J. Geophys. Res., 94(B5), 5716-5728.

See Also

art, kac

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+0.01*rnorm(length(dtrue));

msirt<-sirt(G,d,0.01,200)
par(mfrow=c(1,2))
imagesc(matrix(mtruem,16,16) , asp=1 , main="True Model" );

imagesc(matrix(msirt,16,16) , asp=1 , main="SIRT Solution" );

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