Numerical Analysis Eigenvalues Page 32 CayleyHamilton Theorem 33
- Slides: 63
수치해석 (Numerical Analysis) 고유치 (Eigenvalues)
행렬의 제곱승에 대한 정의 Page 32 Cayley-Hamilton Theorem
파데브-레브리어 알고리즘 개요 (3/3) Faddeev-Leverrier Algorithm 덧붙여, 행렬 A의 역행렬을 다음과 같이 구할 수 있다. 파데브-레브리어 알고리즘의 자세한 증명 과정은 다음을 참조한다. Faddeeva, V. N. , “Computation Methods of Linear Algebra, ” (translated from the Russian by Benster, C. D. ), Dover Publications Inc. , N. Y. , 1959. Page 40
특성 방정식 구하기 - 알고리즘 procedure char_eq(aij: real numbers, n: integer) { [aij] is an nxn matrix. (1 i, j n)} { n is # of columns(= # of rows). } [bij] : = [aij]; n 1 : = trace([bij]); for k : = 2 to n begin [bij] : = [aij] ([bij] + n k+1[iij]); n k : = (1/k) trace([bij]); end return k for every k in between 1 and n; Page 41 Faddeev-Leverrier Algorithm
특성 방정식 구하기 – 프로그램 (1/4) Page 42 Faddeev-Leverrier Algorithm
특성 방정식 구하기 – 프로그램 (2/4) Page 43 Faddeev-Leverrier Algorithm
특성 방정식 구하기 – 프로그램 (3/4) Page 44 Faddeev-Leverrier Algorithm
특성 방정식 구하기 – 프로그램 (4/4) Page 45 Faddeev-Leverrier Algorithm
역행렬 구하기 - 알고리즘 procedure char_inv(aij: real numbers, n: integer) { [aij] is an nxn matrix. (1 i, j n)} { n is # of columns(= # of rows). } [bij] : = [aij]; n 1 : = trace([bij]); for k : = 2 to n begin [bij] : = [aij] ([bij] + n k+1[iij]); n k : = (1/k) trace([bij]); if k = n 1 then [cij] = [bij]; end [rij] : = (1/ 0) ([cij]+ 1[iij]); return [rij]; Page 52 Faddeev-Leverrier Algorithm
역행렬 구하기 – 프로그램 (1/5) Page 53 Faddeev-Leverrier Algorithm
역행렬 구하기 – 프로그램 (2/5) Page 54 Faddeev-Leverrier Algorithm
역행렬 구하기 – 프로그램 (3/5) Page 55 Faddeev-Leverrier Algorithm
역행렬 구하기 – 프로그램 (4/5) Page 56 Faddeev-Leverrier Algorithm
역행렬 구하기 – 프로그램 (5/5) Page 57 Faddeev-Leverrier Algorithm
역행렬 구하기 – 실행 결과 I (2/2) 실행 결과 Page 59 Faddeev-Leverrier Algorithm
역행렬 구하기 – 실행 결과 II (2/2) 실행 결과 Page 61 Faddeev-Leverrier Algorithm
역행렬 구하기 – 실행 결과 III (2/2) 실행 결과 Page 63 Faddeev-Leverrier Algorithm
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