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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.12 No.2
- 발행연도
- 2008.8
- 수록면
- 55 - 68 (14page)
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초록· 키워드
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One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form P(X) = A?X<SUP>m</SUP>+A₁X<SUP>m-1</SUP>+…+A<SUB>m</SUB>, where A?, A₁,…, A<SUB>m</SUB> and X are n × n complex matrices. Newton's method was introduced a useful tool for solving the equation P(X) = 0. Here, we suggest an improved approach to solve each Newton step and consider how to incorporate line searches into Newton's method for solving the matrix polynomial. Finally, we give some numerical experiment to show that line searches reduce the number of iterations for convergence.
목차
ABSTRACT
1. INTRODUCTION
2. THEORY
3. NEWTON‘S METHOD
4. NUMERICAL EXPERIMENTS AND CONCLUSIONS
REFERENCES
참고문헌 (12)
참고문헌 신청
1. [학술지(정기간행물)] - George J. Davis / 1981 / Numerical solution of a quadratic matrix equation / SIAM J. Sci. Stat. Comput 2 : 164 ~ 175
2. [학술지(정기간행물)] - George J. Davis / 1983 / An alogrithm to compute solvents of the matrix equation AX2 +BX +C = 0 / ACM Trans. Math. Software 9 : 246 ~ 254
3. [학술지(정기간행물)] - J. E. Dennis, Jr. / 1976 / The algebraic theory of matrix polynomials / Numerical Algorithms 13 : 831 ~ 845
4. [단행본] - J. E. Dennis, Jr. / 1983 / Numerical Methods for Unconstrained Optimization and Nonlinear Equations / Prentice-Hall, Englewood Cliffs, NJ, USA
5. [학술지(정기간행물)] - N. J. Higham / 2000 / Numerical analysis of a quadratic matrix equation / IMA J. Numer. Anal 20 : 499 ~ 519
2. [학술지(정기간행물)] - George J. Davis / 1983 / An alogrithm to compute solvents of the matrix equation AX2 +BX +C = 0 / ACM Trans. Math. Software 9 : 246 ~ 254
3. [학술지(정기간행물)] - J. E. Dennis, Jr. / 1976 / The algebraic theory of matrix polynomials / Numerical Algorithms 13 : 831 ~ 845
4. [단행본] - J. E. Dennis, Jr. / 1983 / Numerical Methods for Unconstrained Optimization and Nonlinear Equations / Prentice-Hall, Englewood Cliffs, NJ, USA
5. [학술지(정기간행물)] - N. J. Higham / 2000 / Numerical analysis of a quadratic matrix equation / IMA J. Numer. Anal 20 : 499 ~ 519
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UCI(KEPA) : I410-ECN-0101-2009-410-015004563