Abstract:
Linear least squares (LLS) problem is a computational problem of wide scale
importance in the field of numerical linear algebra. Such problem often arises
in real world applications subject to some equality constraints and is known
as linear least squares problem with equality constraints (LSE). In this work,
updating techniques based on QR factorization are considered as a solution
tool for LSE problem. The LSE problem is first transformed into the weighted
LLS problem using a suitable weighted factor w and then its solution is ap
proximated by the updating techniques. The proposed updating algorithms
are mainly based on Householder QR factorization. The original problem
is partition into a small subproblem and then its QR factorization is com
puted. The removed block of columns and rows are appended respectively
and then updated the QR factorization to get the solution of the original
problem. The proposed algorithms contain repeatedly updating of the QR
factorization to approximate the solution of LSE problem. Moreover, the
solution of an equivalent formulation of LSE problem possessing the saddle
point structure is computed using updating of the QR factorization. The
proposed algorithms are implemented in MATLAB and the error analysis
has been carried out to study their accuracy and stability
