lscov

Purpose

Least squares solution in the presence of known covariance.

Synopsis

x = lscov(A,b,V)

Description

x = lscov(A,b,V) returns the vector x that minimizes

(A

*x-b)'*inv(V)*(A*x-b) for the case in which length(b) > length(x). This is the over-determined least squares problem with covariance V. V is a square symmetric matrix with dimensions equal to length(b). The solution is found without inverting V.

Algorithm

The classical linear algebra solution to this problem is

 x = inv(A'*inv(V)*A)*A'*inv(V)*b

but this function computes the QR decomposition of A and then modifies Q by V.

Reference