Jacobi Eigenvalue Method
Jacobi's iteration method for eigenvalues and eigenvectors.
eigjacobi(A, tol = .Machine$double.eps^(2/3))
A |
a real symmetric matrix. |
tol |
requested tolerance. |
The Jacobi eigenvalue method repeatedly performs (Givens) transformations until the matrix becomes almost diagonal.
Returns a list with components V, a matrix containing the
eigenvectors as columns, and D a vector of the eigenvalues.
This R implementation works well up to 50x50-matrices.
Mathews, J. H., and K. D. Fink (2004). Numerical Methods Using Matlab. Fourth edition, Pearson education, Inc., New Jersey.
A <- matrix(c( 1.06, -0.73, 0.77, -0.67,
-0.73, 2.64, 1.04, 0.72,
0.77, 1.04, 3.93, -2.14,
-0.67, 0.72, -2.14, 2.04), 4, 4, byrow = TRUE)
eigjacobi(A)
# $V
# [,1] [,2] [,3] [,4]
# [1,] 0.87019414 -0.3151209 0.1975473 -0.3231656
# [2,] 0.11138094 0.8661855 0.1178032 -0.4726938
# [3,] 0.07043799 0.1683401 0.8273261 0.5312548
# [4,] 0.47475776 0.3494040 -0.5124734 0.6244140
#
# $D
# [1] 0.66335457 3.39813189 5.58753257 0.02098098Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.