[R] Solving a tridiagonal system

[Roger Koenker]

SparseM is really intended for arbitrary sparse structure,
for banded structural there are much more efficient methods,
some of which are, if I'm not mistaken, now available in lapack.


url:	www.econ.uiuc.edu/~roger/my.html	Roger Koenker
email	rkoenker at uiuc.edu			Department of Economics
vox: 	217-333-4558				University of Illinois
fax:   	217-244-6678				Champaign, IL 61820

On Wed, 1 Oct 2003, Thomas W Blackwell wrote:

> Will  -
>
> Take a look at Roger Koenker's package  SparseMatrix,
> available from CRAN.  Look also for some other package
> from Roger which depends on SparseMatrix, but has a
> different name.  It's a place to look.  I don't recall
> whether it will answer your need or not.
>
> -  tom blackwell  -  u michigan medical school  -  ann arbor  -
>
> On Wed, 1 Oct 2003, Will Harvey wrote:
>
> > I need to find solutions to a tridiagonal system. By
> > this I mean a set of linear equations Ax = d where A
> > is a square matrix containing elements A[i,i-1],
> > A[i,i] and A[i,i+1] for i in 1:nrow, and zero
> > elsewhere. R is probably not the ideal way to do this,
> > but this is part of a larger problem that requires R.
> >
> > In my application it is much easier (and much faster)
> > to generate the diagonal and off-diagonal elements of
> > A as vectors, i.e. a = A[i,i-1], b = A[i,i] and c =
> > A[i,i+1]. So I have three vectors that define A, along
> > with a solution vector d. The conventional method of
> > solving such systems is to use the so-called "Thomas
> > algorithm", see e.g.
> > <http://www.enseeiht.fr/hmf/travaux/CD0001/travaux/optmfn/hi/01pa/hyb74/node24.html>.
> > This is very easy to code, but much more difficult to
> > "vectorize". Is anyone aware of a library that
> > contains a fast implementation of this algorithm?
> >
> > Another alternative is to use backsolve. I can easily
> > eliminate the lower diagonal a, but I'm still left
> > with b and c, whereas backsolve requires a matrix.
> > Again, I can write a function to read b and c into a
> > matrix, but this requires loops, and is too slow. Is
> > there a vectorized way of doing it? Of course, the
> > diag command works for b, but what about c? In Octave,
> > diag allows for an offset, but R apparently does not.
> >
> > I would appreciate any and all assistance you experts
> > can offer. Thanks in advance.
> >
> > Will Harvey
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> >
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>