R: Jacobi Eigenvalue Method

eigjacobi {pracma} | R Documentation

## 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.

### Details

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

### Value

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

### Note

This R implementation works well up to 50x50-matrices.

### 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

[Package pracma version 2.0.4 Index]