An analytic parahermitian matrix admits an eigenvalue decomposition (EVD) with eigenvalues and eigenvectors except in the case of multiplexed data. In this paper, we propose iterative algorithm for estimation eigenvalues. Since these are generally transcendental, find a polynomial approximation defined error. Our approach operates discrete Fourier transform (DFT) domain every DFT length generat...

Spectral clustering has attracted much research interest in recent years since it can yield impressively good clustering results. Traditional spectral clustering algorithms first solve an eigenvalue decomposition problem to get the low-dimensional embedding of the data points, and then apply some heuristic methods such as k-means to get the desired clusters. However, eigenvalue decomposition is...

1. Page 2741, caption of Fig. 2: three occurrences of ‘‘commutator’’ instead of ‘‘commutor’’, i.e. the caption should read Fig. 2. Eigenvalue decomposition of the commutor for the CDFT: (a) sorted eigenvalues of the commutor T1 for N 1⁄4 128. (b) Selected symmetric and skew-symmetric eigenvectors of the commutor for k 1⁄4 0,1, 2, 3. 2. Page 2743, fourth sentence after Eq. (14): ‘‘commutator’’ i...

Two adaptive algorithms are presented for robust time delay estimation (TDE) in acoustic environments with a large amount of background noise and reverberation. Recently, an adaptive eigenvalue decomposition (EVD) algorithm has been developed for TDE in highly reverberant acoustic environments. In this paper, we extend the adaptive EVD algorithm to noisy and reverberant acoustic environments, b...

Abstract: Let B ∈ Cn×n denote a finite-dimensional square complex matrix. In [6] and [7], Professor Varga and I introduced Geršgorin-type sets which were developed from Singular Value Decompositions (SVDs) of B. In this note, our work is extended by introducing the polar SV-Geršgorin set, Γ(B). The set Γ(B) is a union of n closed discs in C, whose centers and radii are defined in terms of the e...

We consider a class of singular Schrödinger operators H that act in L2(0,∞), each of which is constructed from a positive function φ on (0,∞). Our analysis is direct and elementary. In particular it does not mention the potential directly or make any assumptions about the magnitudes of the first derivatives or the existence of second derivatives of φ. For a large class of H that have discrete s...

In this paper, we present methods for image compression on the basis of eigenvalue decomposition of normal matrices. The proposed methods are convenient and self-explanatory, requiring fewer and easier computations as compared to some existing methods. Through the proposed techniques, the image is transformed to the space of normal matrices. Then, the properties of spectral decomposition are de...

We first consider the following inverse eigenvalue problem: givenX ∈ Cn×m and a diagonal matrix Λ ∈ Cm×m, find n×nHermite-HamiltonmatricesK andM such thatKX MXΛ. We then consider an optimal approximation problem: given n × n Hermitian matrices Ka and Ma, find a solution K,M of the above inverse problem such that ‖K−Ka‖ ‖M−Ma‖ min. By using the MoorePenrose generalized inverse and the singular v...

spectral decomposition of time series has a significant role in seismic data processing and interpretation. since the earth acts as a low-pass filter, it changes frequency content of passing seismic waves. conventional representing methods of signals in time domain and frequency domain cannot show time and frequency information simultaneously. time-frequency transforms upgraded spectral decompo...

In this paper we give a survey of some results concerning the computation of quadrature formulas on the unit circle. Like nodes and weights of Gauss quadrature formulas (for the estimation of integrals with respect to measures on the real line) can be computed from the eigenvalue decomposition of the Jacobi matrix, Szegő quadrature formulas (for the approximation of integrals with respect to me...