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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.14 No.1
- 발행연도
- 2010.3
- 수록면
- 29 - 34 (6page)
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초록· 키워드
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The QR method is one of the most common methods for calculating the eigenvalues of a square matrix, however its understanding would require complicated and sophisticated mathematical logics. In this article, we present a simple way to understand QR method only with a minimal mathematical knowledge. A deflation technique is introduced, and its combination with the power iteration leads to extracting all the eigenvectors. The orthogonal iteration is then shown to be compatible with the combination of deflation and power iteration. The connection of QR method to orthogonal iteration is then briefly reviewed. Our presentation is unique and easy to understand among many accounts for the QR method by introducing the orthogonal iteration in terms of deflation and power iteration.
목차
ABSTRACT
1. INTRODUCTION
2. POWER ITERATION AND DEFLATED MATRIX
3. ORTHOGONAL ITERATION
4. QR METHOD
ACKNOWLEDGMENTS
REFERENCES
참고문헌 (11)
참고문헌 신청
1. [학술지(정기간행물)] - G. Ammar / 2001 / Polynomial zerofinders based on szego polynomials / J. Comput. Appl. Math. 127 : 1 ~ 16
2. [학술지(정기간행물)] - R. Burnside / 1996 / A simple proof of the transposed qr algorithm / SIAM Review 38 : 306 ~ 308
3. [학술지(정기간행물)] - D. Calvetti / 2002 / The restarted qr-algorithm for eigenvalue computation of structured matrices / J. Comput. Appl. Math. 149 : 415 ~ 422
4. [학술지(정기간행물)] - J. Francis / 1961 / The qr transformation i / Comput. J. 4 : 265 ~ 271
5. [학술지(정기간행물)] - J. Francis / 1961 / The qr transformation ii / Comput. J. 4 : 332 ~ 345
2. [학술지(정기간행물)] - R. Burnside / 1996 / A simple proof of the transposed qr algorithm / SIAM Review 38 : 306 ~ 308
3. [학술지(정기간행물)] - D. Calvetti / 2002 / The restarted qr-algorithm for eigenvalue computation of structured matrices / J. Comput. Appl. Math. 149 : 415 ~ 422
4. [학술지(정기간행물)] - J. Francis / 1961 / The qr transformation i / Comput. J. 4 : 265 ~ 271
5. [학술지(정기간행물)] - J. Francis / 1961 / The qr transformation ii / Comput. J. 4 : 332 ~ 345
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UCI(KEPA) : I410-ECN-0101-2010-410-002236856