Parameterized eigensolution technique for solving constrained least squares problems^∗

^∗This work is supported by Kuwait university contract number SM 158.

Abstract

This paper aims to introduce an algorithm for solving large scale least squares problems subject to quadratic inequality constraints. The algorithm recasts the least squares problem in terms of a parameterized eigenproblem. A variant of k-step Arnoldi method is determined to be well suited for computing the parameterized eigenpair. A two-point interpolating scheme is developed for updating the parameter. A local convergence theory for this algorithm is presented. It is shown that this algorithm is superlinearly convergent.

Keywords:

• Constrained least squares problem
• rational interpolation
• convergence analysis
• parameterized eigenproblems

AMS Classifications Primary::

• 65F15
• Secondary: 65G05

C.R. Category:

• G 1.3

^† On leave from Department of Mathematics, Faculty of Science, Alexandria University, Egypt.

^∗This work is supported by Kuwait university contract number SM 158.

^† On leave from Department of Mathematics, Faculty of Science, Alexandria University, Egypt.

^∗This work is supported by Kuwait university contract number SM 158.

Notes

^† On leave from Department of Mathematics, Faculty of Science, Alexandria University, Egypt.

^∗This work is supported by Kuwait university contract number SM 158.