New Criteria for Judging Generalized Strictly Diagonally Dominant Matrix

Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix.In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.

Criteria Condition for Generalized Diagonally Dominant Matrices

In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.

Criteria Conditions for Generalized Diagonally Dominant Matrices

In this paper, some new sufficient conditions for generalized dominant matrices are given, and some results in [1] are generalized and improved.

Criteria Conditions for Generalized Diagonally Dominant Matrices

In this paper, we provide some new criteria conditions for generalized strictly diagonally dominant matrices, such that the corresponding results in [1] are generalized and improved.

The Estimates of Diagonally Dominant Degree and Eigenvalue Inclusion Regions for the Schur Complement of Matrices

The theory of Schur complement plays an important role in many fields such as matrix theory, control theory and computational mathematics. In this paper, some new estimates of diagonally, α-diagonally and product α-diagonally dominant degree on the Schur complement of matrices are obtained, which improve some relative results. As an application, we present several new eigenvalue inclusion regions for the Schur complement of matrices. Finally, we give a numerical example to illustrate the advantages of our derived results.

The Distribution of Eigenvance of Product Diagonal Dominance Matrix

Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.

Diagonally loaded SMI algorithm based on inverse matrix recursion

The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.

The Tatonnement of Leon Walras and Diagonal Dominant Hypothesis

This essay poses Walras＇s theory of price mechanism in its merits and limitations. Walras proposed two laws as conditions for general equilibrium, namely： （1） the law of the variation of equilibrium prices, a subjective condition; and （2） the law of the establishment of equilibrium prices, an objective condition. Walras jointed both laws in order to develop his law of supply and demand. This paper offers a formal Walrasian approximation in terms of the Lyapounov＇s function, taking the diagonal dominant hypothesis as departure point, rediscovered almost a century after it was originally proposed by Walras. The paper concludes with critical reflection concerning the idea of equilibrium economics as medium of social cohesion.

Recent developments on applications of sequential loop closing and diagonal dominance control schemes to industrial multivariable system

With a focus on an industrial multivariable system, two subsystems including the flow and the level outputs are analysed and controlled, which have applicability in both real and academic environments. In such a case, at first, each subsystem is distinctively represented by its model, since the outcomes point out that the chosen models have the same behavior as corresponding ones. Then, the industrial multivariable system and its presentation are achieved in line with the integration of these subsystems, since the interaction between them can not actually be ignored. To analyze the interaction presented, the Gershgorin bands need to be acquired, where the results are used to modify the system parameters to appropriate values. Subsequently, in the view of modeling results, the control concept in two different techniques including sequential loop closing control(SLCC) scheme and diagonal dominance control(DDC) schemes is proposed to implement on the system through the Profibus network, as long as the OPC(OLE for process control) server is utilized to communicate between the control schemes presented and the multivariable system. The real test scenarios are carried out and the corresponding outcomes in their present forms are acquired. In the same way, the proposed control schemes results are compared with each other, where the real consequences verify the validity of them in the field of the presented industrial multivariable system control.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

Necessary and Sufficient Condition for Generalized Diagonal Dominance Matrices

In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in the references are corrected.

GH-CONGRUENCE CANONICAL FORM OF QUATERNION MATRIX AND SIMULTANEOUS DIAGONALIZATION OF MATRICES

In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruence for two positive semidifinite(definite)quaternion matrices isgiven also.Then simultaneous GH-congruence reduced forms for two self-conjugate matri-ces and some result about the simultaneous GH-congruence diagonalization of quaternionmatrices are obtained.

Decoupling Control Research on Test System of Hydraulic Drive Unit of Quadruped Robot Based on Diagonal Matrix Method

The mathematical model of hydraulic drive unit of quadruped robot was built in this paper. According to the coupling characteristics between position control system and force control system, the decoupling control strategy was realized based on diagonal matrix method in AMESim?. The results of simulation show that using diagonal matrix method can achieve the decoupling control effectively and it can achieve the decoupling control more effectively with the method of not offset pole-zero in the S coordinate. This research can provide theoretical basis for the application of test system of hydraulic drive unit.

Realization of Robust Diagonal Dominance

In this paper, the realization of diagonal dominance in an uncertain system is discussed. First, the sufficient and necessary conditions are formulated for a deterministic system to realize diagonal dominance. Secondly, the conditions for realizing robust diagonal dominance in the system where exist perturbation are given. Finally, an illustrative example is provided to demonstrate the effectiveness of this method.

On Classes of Matrices with Variants of the Diagonal Dominance Property

We study the relations between several classes of matrices with variants of the diagonal dominance property, and identify those classes which form pairs of incomparable classes. For an incomparable pair (X1,X2) of classes of matrices with variants of the diagonal dominance property, we also study the problem of providing sufficient conditions for the matrices in Xi to be in Xj with {i,j}={1,2}. The article is a continuation of a series of articles on the topic and related topics by the author;see [1][2][3][4].

Oversample Reconstruction Based on a Strong Inter-Diagonal Matrix for an Optical Microscanning Thermal Microscope Imaging System

Based on a strong inter-diagonal matrix and Taylor series expansions,an oversample reconstruction method was proposed to calibrate the optical micro-scanning error. The technique can obtain regular 2 ×2 microscanning undersampling images from the real irregular undersampling images,and can then obtain a high spatial oversample resolution image. Simulations and experiments show that the proposed technique can reduce optical micro-scanning error and improve the system＇s spatial resolution. The algorithm is simple,fast and has low computational complexity. It can also be applied to other electro-optical imaging systems to improve their spatial resolution and has a widespread application prospect.

A New Approximation to the Linear Matrix Equation AX = B by Modification of He’s Homotopy Perturbation Method

It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

REMARKS ON BRUALDI'S THEOREM FOR SPECTRUM INCLUSION REGION OF AN IRREDUCIBLE MATRIX

This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.