Direct sequential evaluation of Hermite-Gaussian-like eigenvectors of the DFT matrix
Magdy Tawfik Hanna · 2009
The generation of orthonormal eigenvectors of a unitary matrix exemplified by the DFT matrix that are close to approximate desired eigenvectors - such as those formed by samples of the Hermite Gaussian functions - is formulated as a c. The unitarity of the matrix implies the orthogonality of its eigenspaces pertaining to its distinct eigenvalues and consequently orthonormal basis are sought for each eigenspace separately. The method advocated here is based on solving a series of constrained minimization problems where in each stage one eigenvector is generated by minimizing the squared Euclidian norm of the error between that vector and its approximate counterpart subject to the constraints that this eigenvector is orthogonal to the previously evaluated ones.