Level-2 condition numbers for least-squares solution of Kronecker product linear systems

Abstract

Kronecker product linear systems arise more and more often in the real world. In this paper, we consider the minimum norm least-squares solution of Kronecker product linear systems (A⊗ B)x=b by extending some known results from nonsingular cases to singular or rectangular cases. We investigate the level-2 condition numbers, and the corresponding bounds of these condition numbers.

Keywords:

• Condition numbers
• Generalized inverse
• Kronecker product linear systems
• Least-squares solution
• Level-2 condition numbers

AMS Subject Classification:

• 15A12
• 65F20

Acknowledgements

This project is supported by the National Natural Science Foundation of China under grant 10471027 and the Shanghai Education Committee.

Additional information

Notes on contributors

Hua Xiang

Current address: INRIA Futurs, Parc Club Orsay Universite, 4 rue Jacques Monod, 91893 Orsay Cedex France.