Solving equality constrained least squares problems

Constrained least squares problems occur often in practice, mostly as sub-problems in many optimization contexts. For solving large and sparse instances of these problems on parallel architectures with distributed memory, the use of static data structures to represent the sparse matrix is preferred during the factorization. But the accurate detection of the rank of the constraint matrix is also very critical to the accuracy of the computed solution. The author examines the solution of the constrained problem using weighting approach. All computations can be carried out using a static data structure that is generated using the symbolic structure of the input matrices, making use of a recently proposed rank detection procedure. The author shows good speed-ups in solving large and sparse equality conditioned least squares problems on hypercubes of up to 128 processors