1ccc1ea8-80f4-4ed7-b0c4-4af91f6eb09b 21 Martin Kraska 3 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Vektoriteration für das allgemeine Eigenwertproblem

http://www.rzbt.haw-hamburg.de/dankert/WWWErgVert/html/vektoriteration_fur_das_allgem.html

VI(A,B) Computes the smallest Eigenvalue λ and the corresponding eigenvector v of the general eigenvalue problem (A-λB)v=0 with square matrices A and B using iterated vectors. Thereturn value is a row vector (λ,v,n) with n being the number of iterations required to meet the precision given by ε in the function. n is limited to 100. A# B VI A# B 100 VI :

VI(A,B,maxit) Computes the smallest Eigenvalue λ and the corresponding eigenvector v of the general eigenvalue problem (A-λB)v=0 with square matrices A and B using iterated vectors. Thevalue is a row vector (λ,v,n) with n being the number of iterations required to meet the precisiongiven by ε in the function. n is limited to maxit. A# B maxit VI ε 108 -^: z A# rows 1 Ones : r.alt z : λ 0 : i 1 maxit range r B z * eval : z A# 1 -^r * eval : λ.min z r.alt * z r * / eval : λ.min λ - λ.min λ + / abs ε < break 0 if λ λ.min : r.alt r z max / : z z z max / : 71 line for z z z max / : λ.min z i 13 mat 71 line :

Beispiel aus Dankert/Dankert S. 419

λ.min z i 13 mat 54 - 14 - 64 - 14 - 533 mat 2 1.5 - 0 1.5 - 4 2.5 - 0 2.5 - 633 mat VI : 0.2742 0.6261 1 0.8014 31 mat 813 mat

Beispiel Rust S.15

l 1 :

A 0.01 l * (2^:

E 1000000 :

F 10 :

I A 0.01 l * (2^* :

L E l / A 00012 I l 2^/ * 6 I l / * - 06 I l / * - 4 I * 33 mat * 0000 F l / 000033 mat VI : #

3 appVersion 1.0.8348

lastError Die Eingabezeichenfolge hat das falsche Format.

F.k L 1 el F * : E I * l 2^/ #

lastError L - not defined.