Parameterized eigensolution technique for solving constrained least squares problems

This paper aims to introduce an algorithm for solving large scale least squ ares problems subject to quadratic inequality constraints. The algorithm re casts the least squares problem in terms of a parameterized eigenproblem. A variant of k-step Arnoldi method is determined to be well suited for compu ting the parameterized eigenpair. A two-point interpolating scheme is devel oped for updating the parameter. A local convergence theory for this algori thm is presented. It is shown that this algorithm is superlinearly converge nt.