Bounds for Polynomial’s Roots from Fiedler and Sparse Companion Matrices for Submultiplicative Matrix Norms

We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial P(X) over the field C[X]. From a n×n Fiedler companion matrix C, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix Lr, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of Lr, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.

HIGH PERFORMANCE SPARSE SOLVER FOR UNSYMMETRICAL LINEAR EQUATIONS WITH OUT-OF-CORE STRATEGIES AND ITS APPLICATION ON MESHLESS METHODS

A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.

Modeling of a Planar Nine-Way Metamaterial Power Divider/Combiner

Analysis of the scattering parameters（S-parameters） of planar N-way metamaterial power dividers/combiners mostly uses commercial microwave circuit simulators due to the large circuit size involved. This paper presents an efficient circuit modeling approach, which is based on the multi-input and multi-output transmission matrix（T-matrix） method, to analyze the S-parameter of a planar nine-way metamaterial power-divider/combiner structure. S-parameter computation results are shown in good agreement with the simulation results by using the Agilent advanced design system（ADS） and measurement results. The computation time of an N-way metamaterial power divider/combiner with N=5, 9, 13, and 17 using T-matrix method is also compared with those of ADS and AWR Microwave Office（MWO） to demonstrate its computational efficiency.

A Compact Heart Iteration for Large Eigenvalues Problems

In this paper, we present a compact version of the Heart iteration. One that requires less matrix-vector products per iteration and attains faster convergence. The Heart iteration is a new type of Restarted Krylov methods for calculating peripheral eigenvalues of symmetric matrices. The new framework avoids the Lanczos tridiagonalization process and the use of implicit restarts. This simplifies the restarting mechanism and allows the introduction of several modifications. Convergence is assured by a monotonicity property that pushes the computed Ritz values toward their limits. Numerical experiments illustrate the usefulness of the proposed approach.

A novel sparse feature extraction method based on sparse signal via dual-channel self-adaptive TQWT

Sparse signal is a kind of sparse matrices which can carry fault information and simplify the signal at the same time.This can effectively reduce the cost of signal storage,improve the efficiency of data transmission,and ultimately save the cost of equipment fault diagnosis in the aviation field.At present,the existing sparse decomposition methods generally extract sparse fault characteristics signals based on orthogonal basis atoms,which limits the adaptability of sparse decomposition.In this paper,a self-adaptive atom is extracted by the improved dual-channel tunable Q-factor wavelet transform(TQWT)method to construct a self-adaptive complete dictionary.Finally,the sparse signal is obtained by the orthogonal matching pursuit(OMP)algorithm.The atoms obtained by this method are more flexible,and are no longer constrained to an orthogonal basis to reflect the oscillation characteristics of signals.Therefore,the sparse signal can better extract the fault characteristics.The simulation and experimental results show that the selfadaptive dictionary with the atom extracted from the dual-channel TQWT has a stronger decomposition freedom and signal matching ability than orthogonal basis dictionaries,such as discrete cosine transform(DCT),discrete Hartley transform(DHT)and discrete wavelet transform(DWT).In addition,the sparse signal extracted by the self-adaptive complete dictionary can reflect the time-domain characteristics of the vibration signals,and can more accurately extract the bearing fault feature frequency.

PRECONDITIONING BLOCK LANCZOS ALGORITHM FOR SOLVING SYMMETRIC EIGENVALUE PROBLEMS

A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of block Lanczos algorithm is suitable for determination of the extreme eigenvalues as well as their multiplicities. The global convergence and the asymptotically quadratic convergence of the new method are also demonstrated. [ABSTRACT FROM AUTHOR]

Salt and pepper noise removal in surveillance video based on low-rank matrix recovery

This paper proposes a new algorithm based on low-rank matrix recovery to remove salt &pepper noise from surveillance video. Unlike single image denoising techniques, noise removal from video sequences aims to utilize both temporal and spatial information. By grouping neighboring frames based on similarities of the whole images in the temporal domain, we formulate the problem of removing salt &pepper noise from a video tracking sequence as a lowrank matrix recovery problem. The resulting nuclear norm and L1-norm related minimization problems can be efficiently solved by many recently developed methods. To determine the low-rank matrix, we use an averaging method based on other similar images. Our method can not only remove noise but also preserve edges and details. The performance of our proposed approach compares favorably to that of existing algorithms and gives better PSNR and SSIM results.