klin.ls: Solves a least squares problem where the matrix is a...
In klin: Linear equations with Kronecker structure

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Computes the least squares estimate x which minimizes the Euclidian norm of A %x% x - b, where A is a Kronecker product of matrices.

1	klin.ls(A, b)

`A`	A list that contains the matrices, preferably of class `Matrix`, or a list of class `klin.prepls` (see Details).
`b`	A conformable numeric vector.

The matrices in the list A should be of the class Matrix. This allows the user to take advantage of their special structure (eg sparsity).

This function is just glue for klin.preparels and klin.solve. If you are using the same A multiple times, it is suggested that you call klin.preparels and save the result. This allows Matrix to memoize the factors of crossprod(A[[i]]) where needed.

A numeric vector.

The algorithm (given in the reference) is orders of magnitude more efficient (both in terms of CPU and memory usage) than computing the Kronecker product and calling crossprod and solve.

Tamas K Papp <tpapp@princeton.edu>

Paul E. Buis and Wayne R. Dyksen. Efficient Vector and Parallel Manipulation of Tensor Products. ACM Transactions on Mathematical Software, Vol. 22, No. 1, March 1996, Pages 18–23.

klin.eval, klin.solve, klin.preparels, klin.klist.

## dimensions
n <- c(2,4,3)
m <- n+c(1,0,2)			# we need m >= n
## make random matrices
A <- lapply(seq_along(n),
            function(i) Matrix(rnorm(m[i]*n[i]),m[i],n[i]))
b <- rnorm(prod(m))		# make random b
x <- klin.ls(A,b)