Examples of EigenPowerMethod

org.ejml.alg.dense.decomposition.eig.EigenPowerMethod

The power method is an iterative method that can be used to find dominant eigen vector in a matrix. Computing Aⁿq for larger and larger values of n, where q is a vector. Eventually the dominant (if there is any) eigen vector will "win".

Shift implementations find the eigen value of the matrix B=A-pI instead. This matrix has the same eigen vectors, but can converge much faster if p is chosen wisely.

See section 5.3 in "Fundamentals of Matrix Computations" Second Edition, David S. Watkins.

WARNING: These functions have well known conditions where they will not converge or converge very slowly and are only used in special situations in practice. I have also seen it converge to none dominant eigen vectors.

@author Peter Abeles

     * @param A A matrix.  Not modified.
     */
    // TODO maybe do the regular power method, estimate the eigenvalue, then shift invert?
    public static Eigenpair dominantEigenpair( DenseMatrix64F A ) {


        EigenPowerMethod power = new EigenPowerMethod(A.numRows);


        // eh maybe 0.1 is a good value.  who knows.
        if( !power.computeShiftInvert(A,0.1) )
            return null;


        return null;//power.getEigenVector();
    }

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Examples of EigenPowerMethod

Examples of org.ejml.alg.dense.decomposition.eig.EigenPowerMethod