East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

THE CONDITION NUMBERS OF A QUADRATIC MATRIX EQUATION

  • Kim, Hye-Yeon (Department of Mathematics, Pusan National University) ;
  • Kim, Hyun-Min (Department of Mathematics, Pusan National University)
  • Received : 2013.04.04
  • Accepted : 2013.04.18
  • Published : 2013.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we consider the quadratic matrix equation which can be defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown complex matrix, and A, B and C are $n{\times}n$ given matrices with complex elements. We first introduce a couple of condition numbers of the equation Q(X) and present normwise condition numbers. Finally, we compare the results and some numerical experiments are given.

Keywords

References

  1. G. J. Davis, Numerical solution of a quadratic matrix equation, SIAM J. Sci. Stat. Comput., 2 (1981), 164-175. https://doi.org/10.1137/0902014
  2. I. Gohberg and I. Koltracht, Mixed, componentwise, and structured condition numbers, SIAM J. Matrix Anal. Appl., 14 (1993), 688-704. https://doi.org/10.1137/0614049
  3. N. J. Higham and Hyum-Min Kim, Solving a quadratic matrix equation by Newton's method with line searches, SIAM J. Matrix Anal. Appl., 23 (2001),, 303-316. https://doi.org/10.1137/S0895479899350976
  4. R. Horn and C. Johnson, Topics in Matrix Analysis, Cambridge University Press, (1995).
  5. Yiqin Lin and Yimin Wei, Condition Numbers of the Generalized Sylvester Equation, IEEE Transactions on Automatic Control, 52 (2007), 2380-2385. https://doi.org/10.1109/TAC.2007.910727
  6. R. D. Skeel, Scaling for numerical stablity in Gaussian elimination, J. Assoc. Comput. Mach., 26 (1979), 494-526. https://doi.org/10.1145/322139.322148