East Asian mathematical journal

  • 제29권5호
  • /
  • Pages.511-519
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  • 2013
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  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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THE BINOMIAL METHOD FOR A MATRIX SQUARE ROOT

  • Kim, Yeon-Ji (Department of Mathematics, Pusan National University) ;
  • Seo, Jong-Hyeon (Department of Mathematics, Pusan National University) ;
  • Kim, Hyun-Min (Department of Mathematics, Pusan National University)
  • 투고 : 2013.10.16
  • 심사 : 2013.10.24
  • 발행 : 2013.11.30
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초록

There are various methods for evaluating a matrix square root, which is a solvent of the quadratic matrix equation $X^2-A=0$. We consider new iterative methods for solving matrix square roots of M-matrices. Particulary we show that the relaxed binomial iteration is more efficient than Newton-Schulz iteration in some cases. And we construct a formula to find relaxation coefficients through statistical experiments.

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참고문헌

  1. G.W. Cross and P.Lancaster. Square roots of complex matrices. Linear and Multilinear Algebra, 1:289-293, 1974. https://doi.org/10.1080/03081087408817029
  2. C.-H. Guo and N. J. Higham. Iterative solution of a nonsymmetric algebraic Riccati equation. SIAM J. Matrix Anal. Appl., 29:396-412, 2007. https://doi.org/10.1137/050647669
  3. N. J. Higham. Newton's method for the matrix square root. Math. Comput., 46(174):537-549, 1986.
  4. N. J. Higham. Stable iterations for the matrix square root. Numer. Algorithms, 15:227- 242, 1997. https://doi.org/10.1023/A:1019150005407
  5. N. J. Higham. Functions of matrices: theory and computation. SIAM, 2008.
  6. R. A. Horn and C. R. Johnson. Matrix analysis. Cambridge University Press, 1985.
  7. R. A. Horn and C. R. Johnson. Topics in matrix analysis. Cambridge University Press, 1994.
  8. Charles Kenney and Alan J. Laub. Rational iterative methods for the matrix sign function. SIAM Journal on Matrix Analysis and Applications, 12:273-291, 1991. https://doi.org/10.1137/0612020
  9. Hyun-Min Kim. Numerical methods for solving a quadratic matrix equation. Master's thesis, Department of Mathematics, University of Manchester, 2000.
  10. J. D. ROBERTS. Linear model reduction and solution of the algebraic riccati equation by use of the sign function. International Journal of Control, 32:677-687, 1980. https://doi.org/10.1080/00207178008922881
  11. Gilbert Strang. Linear Algebra and Its Applications. Thomson Brooks/Cole Cengage learning, 2006.