I want to solve a regularized least squares
problem of the form
min ||Ax-b|| + lambda * ||x||^2
using recursive least squares, i.e. upadting
the solution x once new observed
data (a',b*) arrives:
min || [A; a'] x -[b;b*] || + lambda* ||x||^2
The data matrix A is usually a tall (n x m) matrix.
Recursive least squares works by updating
the inverse of the cross-product matrix:
B:=(A'*A + lambda*I)^(-1)
using rank-1 updates of the form
If the data matrix A is a dense matrix I can use the
BLAS function ?ger and everything works fine.
My problem is that A is a sparse matrix, and the newly
arriving data a' is a sparse vector.
Perhaps I miss something very important, but I couldn't
find a sparse rank-1 update. Any suggestions?
Thanks in advance.