pracma (version 1.9.9)

eigjacobi: Jacobi Eigenvalue Method

Description

Jacobi's iteration method for eigenvalues and eigenvectors.

Usage

eigjacobi(A, tol = .Machine$double.eps^(2/3))

Arguments

A

a real symmetric matrix.

tol

requested tolerance.

Value

Returns a list with components V, a matrix containing the eigenvectors as columns, and D a vector of the eigenvalues.

Details

The Jacobi eigenvalue method repeatedly performs (Givens) transformations until the matrix becomes almost diagonal.

References

Mathews, J. H., and K. D. Fink (2004). Numerical Methods Using Matlab. Fourth edition, Pearson education, Inc., New Jersey.

See Also

eig

Examples

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 0.02098098