an infinity norm bound for the inverse of dashnic zusmanovich type matrices with applications abstract an upper bound for the infinity norm for the inverse of dashnic zusmanovich type matrices is given it is proved that the upper bound is sharper than the well known varah s bound for strictly diagonally dominant matrices by introducing a new subclass of p matrices dashnic zusmanovich type b matrices dz type b matrices and using the proposed infinity norm bound an error bound is given for the linear complementarity problems of dz type b matrices we also give a new pseudospectra localization to measure the distance to instability

balanced truncation for temporal and spatial lpv interconnected systems based on the full block s procedure abstractthis paper presents a technique for model order reduction of exponentially stable temporal and spatial lpv linear parameter varying interconnected systems represented in linear fractiona

decoding least effort and scaling in signal frequency distributions abstract here assuming a general communication model where objects map to signals a power function for the distribution of signal frequencies is derived the model relies on the satisfaction of the receiver hearer communicative needs when the entropy of the number of objects per signal is maximized evidence of power distributions in a linguistic context some of them with exponents clearly different from the typical 2 of zipf s law is reviewed and expanded we support the view that zipf s law reflects some sort of optimization but following a novel realistic approach where signals e g words are used according to the objects e g meanings they are linked to our results strongly suggest that many systems in nature use non trivial strategies for easing the interpretation of a signal interestingly constraining just the number of interpretations of signals does not lead to scaling

special h matrices and their schur and diagonal schur complements it is well known see d carlson t markham schur complements of diagonally dominant matrices czech math j 29 104 1979 246 251 2 j liu j li z huang x kong some properties of schur complements and diagonal schur complements of diagonally dominant matrices linear alg appl 428 2008 1009 1030 14 that the schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant as well as its diagonal schur complement also if a matrix is an h matrix then its schur complement and diagonal schur complement are h matrices too see j liu y huang some properties on schur complements of h matrices and diagonally dominant matrices linear alg appl 389 2004 365 380 13 recent research see j liu y huang f zhang the schur complements of generalized doubly diagonally dominant matrices linear alg appl 378 2004 231 244 12 j liu j li z huang x kong some properties of schur complements and diagonal schur complements of diagonally dominant matrices linear alg appl 428 2008 1009 1030 14 showed that the similar statements hold for some special subclasses of h matrices the aim of this paper is to give more invariance results of this type and simplified proofs for some already known results by using scaling approach

on the convergence of a class of parallel decomposition type relaxation methods a class of parallel decomposition type accelerated overrelaxation methods suitable to the simd systems is established and sufficient and or necessary conditions ensuring its convergence are concluded when the coefficient matrices of the linear systems of equations are respectively l matrices h matrices and symmetric positive definite matrices

a kalman decomposition for possibly controllable uncertain linear systems this paper considers the structure of uncertain linear systems building on concepts of robust unobservability and possible controllability the paper presents a new geometric characterization of the possibly controllable states when combined with previous geometric results on robust unobservability the results of this paper lead to a general kalman type decomposition for uncertain linear systems which can be applied to the problem of obtaining reduced order uncertain system models

computation of error bounds for p matrix linear complementarity problems we give new error bounds for the linear complementarity problem where the involved matrix is a p matrix computation of rigorous error bounds can be turned into a p matrix linear interval system moreover for the involved matrix being an h matrix with positive diagonals an error bound can be found by solving a linear system of equations which is sharper than the mathias pang error bound preliminary numerical results show that the proposed error bound is efficient for verifying accuracy of approximate solutions

parallel hybrid iteration methods for block bordered linear systems a class of parallel hybrid iteration method and its accelerated overrelaxation variant are established for solving the large sparse block bordered system of linear equations and their convergence are proved when the coefficient matrix of the linear system is an m matrix an h matrix and a symmetric positive definite matrix respectively

a framework for robustness analysis of constrained finite receding horizon control a framework for robustness analysis of input constrained finite receding horizon control is presented under the assumption of quadratic upper bounds on the finite horizon costs we derive sufficient conditions for robust stability of the standard discrete time linear quadratic receding horizon control formulation this is achieved by recasting conditions for nominal and robust stability as an implication between quadratic forms lending itself to s procedure tools which are used to convert robustness questions to tractable convex conditions robustness with respect to plant model mismatch as well as for state measurement error is shown to reduce to the feasibility of linear matrix inequalities simple examples demonstrate the approach

error bounds for linear complementarity problems of db matrices doubly b matrices db matrices which properly contain b matrices are introduced by pena 2003 2 in this paper we present error bounds for the linear complementarity problem when the matrix involved is a db matrix and a new bound for linear complementarity problem of a b matrix the numerical examples show that the bounds are sharp

upper bounds for the infinity norm of the inverse of sdd and s sdd matrices an easily calculable upper bound for the infinity norm of the inverse of s strictly diagonally dominant s sdd matrices introduced by gao and wang in 1992 is obtained in this paper applying that bound to sdd matrices we improve the varah bound we also introduce an iterative procedure for obtaining sharper bounds accompanied with some open questions

infinity norm bounds for the inverse of nekrasov matrices from the application point of view it is important to have a good upper bound for the maximum norm of the inverse of a given matrix a in this paper we will give two simple and practical upper bounds for the maximum norm of the inverse of a nekrasov matrix

robust stability analysis of time varying systems using time varying quadratic forms abstract we consider the robust stability of time varying linear systems subject to structured time varying uncertainty we provide an alternate proof of the result that robust stability holds if and only if a scaled small gain condition holds asymptotically the new proof employs an extension of the so called s procedure losslessness theorem to time varying quadratic forms which is of independent interest

error bounds for the linear complementarity problem with a p matrix abstract we introduce a fundamental quantity associated with a p matrix and show how this quantity is useful in deriving error bounds for the linear complementarity problem of the p type we also obtain upper and lower bounds for the quantity introduced

structured noncommutative multidimensional linear systems we introduce a class of multidimensional linear systems with evolution along a free semigroup the transfer function for such a system is a formal power series in noncommuting indeterminates standard system theoretic properties the operations of cascade parallel connection and inversion controllability observability kalman decomposition state space similarity theorem minimal state space realizations hankel operators realization theory are developed for this class of systems we also draw out the connections with the much earlier studied theory of rational and recognizable formal power series applications include linear fractional models for classical discrete time systems with structured time varying uncertainty dimensionless formulas in robust control multiscale systems and automata theory and the theory of formal languages

max norm estimation for the inverse of block matrices abstract maximum norm bound of the inverse of a given matrix is an important issue in a wide range of applications motivated by this fact we will extend the list of matrix classes for which upper bounds for max norms can be obtained these classes are subclasses of block h matrices and they stand in a general position with corresponding point wise classes efficiency of new results will be illustrated by numerical examples

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

infinity norm bounds for the inverse of nekrasov matrices using scaling matrices abstract for many applications it is convenient to have good upper bounds for the norm of the inverse of a given matrix in this paper we obtain such bounds when a is a nekrasov matrix by means of a scaling matrix transforming a into a strictly diagonally dominant matrix numerical examples and comparisons with other bounds are included the scaling matrices are also used to derive new error bounds for the linear complementarity problems when the involved matrix is a nekrasov matrix these error bounds can improve considerably other previous bounds

a note on eventually sdd matrices and eigenvalue localization it is shown by a counterexample that an eigenvalue localization set for matrices involved with a positive integer k as one of the main theorems provided by cvetkovic et al 2015 does not hold in general for the case that k is odd and then a new eigenvalue localization set for matrices which is a correction of this set is given

the dominant degree and disc theorem for the schur complement of matrix the theory of schur complement plays an important role in many fields such as control theory and computational mathematics in this paper we obtain some estimates for the diagonally c diagonally and product c diagonally dominant degree on the schur complement of matrices which improve some relative results as application we present some bounds for the eigenvalues of schur complement by the entries of the original matrix instead of those of the schur complement particularly we obtain that the eigenvalues of the schur complements are located in the gerschgorin circles of the original matrices under certain conditions

necessary and sufficient conditions of stability a multiloop generalization of the circle criterion a linear time invariant system with a vector output and a vector input is described this system is closed by an uncertain nonlinear time varying feedback the only information on this feedback is given by several integral quadratic inequalities i e the uncertainties under consideration generalize the so called conic nonlinearities necessary and sufficient frequency domain conditions of stability are obtained an advanced version of the s procedure losslessness theorem and some other tools of the absolute stability theory are used

dashnic zusmanovich type matrices a new subclass of nonsingular h matrices abstract a new class of matrices called dashnic zusmanovich type dz type matrices which is similar to but different from dashnic zusmanovich dz matrices is introduced and proved to be a subclass of nonsingular h matrices the relations between strictly diagonally dominant matrices doubly strictly diagonally dominant matrices dz matrices and dz type matrices are discussed finally by the non singularity of dz type matrices a new eigenvalue localization set for matrices is given

fractal geometry information growth and nonextensive thermodynamics abstract this is a study of the information evolution of complex systems by a geometrical consideration we look at chaotic systems evolving in fractal phase space the entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement due to the incompleteness of the state number counting at any scale on fractal support the incomplete normalization i p i q 1 is applied throughout the paper where q is the fractal dimension divided by the dimension of the smooth euclidean space in which the fractal structure of the phase space is embedded it is shown that the information growth is nonadditive and is proportional to the trace form i p i i p i q which can be connected to several nonadditive entropies this information growth can be extremized to give power law distributions for these nonequilibrium systems it can also be used for the study of the thermodynamics derived from tsallis entropy for nonadditive systems which contain subsystems each having its own q it is argued that within this thermodynamics the stefan boltzmann law of blackbody radiation can be preserved

generalized mixed μ bounds for real and complex multiple block uncertainty with internal matrix structure new absolute stability results that unify and extend existing structured singular value bounds for mixed uncertainty are developed using frequency domain arguments these bounds generalize prior upper bounds for mixed by permitting the treatment of non diagonal real uncertain blocks as well as accounting for internal matrix structure in the uncertainty several specializations to well known absolute stability criteria from the classical literature are given which allow for a systematic comparison of these results in addressing the problem of robust stability for real parameter uncertainty

on nekrasov matrices abstract in this paper we investigate nonsingularity of a generalized nekrasov matrix and present some sufficient conditions for this matrix to be nonsingular on one hand on the other hand we also establish some sufficient and necessary conditions for a diagonally dominant matrix or a generalized nekrasov matrix to be a generalized diagonally dominant matrix all results in this presentation improve and generalize the corresponding results of huang t huang linear algebra appl 225 1995 237 and szulc t szulc linear algebra appl 225 1995 221

structure preserving model reduction for spatially interconnected systems with experimental validation on an actuated beam abstracta technique for model reduction of exponentially stable spatially interconnected systems is presented where the order of the reduced model is determined by the number of truncated small generalised singular values of the structured solutions to a pair of lyapunov inequalities for parameter invariant spatially interconnected systems the technique is based on solving a pair of lyapunov inequalities in continuous time and space domain with a rank constraint using log det and cone complementarity methods an improved error bound can be obtained the approach is extended to spatially parameter varying systems and a balanced truncation approach using parameter dependent gramians is proposed to reduce the conservatism caused by the use of constant gramians this is done by considering two important operators which can be used to represent multidimensional systems temporal and spatial linear parameter varying interconnected systems the results are illustrated with their application to an experi

global renyi index of the distance matrix abstract in previous studies the heterogeneity of complex networks has been extensively studied in our study the heterogeneity of distance matrices is studied based on the renyi index of networks we define a new metric and name it global renyi index g r i and prove several properties in particular the g r i value of the distance matrix corresponding to the evenly distributed point set in the euclidean space is zero some model data were used to clarify the geometric meanings of g r i and then we studied the g r i value of financial data the results show that the g r i value in the real market changes drastically and is significantly different from the g r i value of the model generated data these results suggest that the proposed concept g r i is meaningful to the study distance matrix and provides a new perspective based on the network

infimum of error bounds for linear complementarity problems of σ sdd and σ1 ssd matrices abstract in 2013 18 garcia esnaola and pena presented error bounds for the linear complementarity problems of sdd and 1 ssd matrices respectively these bounds all involve a parameter on an open interval it is shown in this paper that the infimum of these error bounds as a function of the parameter exists and then is determined numerical examples are given to verify the theoretical results

accurate inverses of nekrasov z matrices abstract we present a parametrization of a nekrasov z matrix that allows us to compute its inverse with high relative accuracy numerical examples illustrating the accuracy of the method are included

a new approach for analysis and synthesis of time varying systems in this paper new techniques are developed for the analysis of linear time varying ltv systems these lead to a formally simple treatment of robust control problems for ltv systems allowing methods more usually restricted to time invariant systems to be employed in the time varying case as an illustration of this methodology the so called h sub spl infin synthesis problem is solved for ltv systems

a class of parallel hybrid two stage iteration methods for block bordered linear systems a class of parallel hybrid two stage iteration method and its accelerated overrelaxation variant are established for solving the large sparse block bordered system of linear equations and their convergence are proved when the coefficient matrix of this linear system is an m matrix and an h matrix respectively

bounds for norms of the matrix inverse and the smallest singular value abstract in the first part we obtain two easily calculable lower bounds for a 1 where is an arbitrary matrix norm in the case when a is an m matrix using first row sums and then column sums using those results we obtain the characterization of m matrices whose inverses are stochastic matrices with different approach we give another easily calculable lower bounds for a 1 and a 1 1 in the case when a is an m matrix in the second part using the results from the first part we obtain our main result an easily calculable upper bound for a 1 1 in the case when a is an sdd matrix thus improving the known bound all mentioned norm bounds can be used for bounding the smallest singular value of a matrix

classes of general h matrices let m a denote the comparison matrix of a square h matrix a that is m a is an m matrix h matrices such that their comparison matrices are nonsingular are well studied in the literature in this paper we study characterizations of h matrices with either singular or nonsingular comparison matrices the spectral radius of the jacobi matrix of m a and the generalized diagonal dominance property are used in the characterizations finally a classification of the set of general h matrices is obtained

information entropy and power law distributions for chaotic systems the power law is found for density distributions for the chaotic systems of most different nature physical geophysical biological economical social etc on the basis of the maximum entropy principle for the renyi entropy its exponent q is expressed as a function q of the renyi parameter the difference between the renyi and boltzmann shannon entropies a modified lyapunov functional r for the same power law distribution is negative and as a function of has a well defined minimum at which remains within the narrow range from 1 5 to 3 when varying other characteristic parameters of any concrete systems relevant variations of the exponent q are found within the range 1 3 5 the same range of observable values of q is typical for the various applications where the power law distribution takes place it is known under the following names triangular or trapezoidal in physics and technics gutenberg richter law in geophysics zipf pareto law in economics and the humanities lotka low in science of science etc as the negative r indicates self organisation of the system the negative minimum of r corresponds to the most self organised state thus the comparison between the calculated range of variations of q and observable values of the exponent q testifies that the most self organised states are as a rule realised regardless of the nature of a chaotic system

the nekrasov diagonally dominant degree on the schur complement of nekrasov matrices and its applications abstract in this paper we estimate the nekrasov diagonally dominant degree on the schur complement of nekrasov matrices as an application we offer new bounds of the determinant for several special matrices which improve the related results in certain case further we give an estimation on the infinity norm bounds for the inverse of schur complement of nekrasov matrices finally we introduce new methods called schur based super relaxation iteration sssor method and schur based conjugate gradient scg method to solve the linear equation by reducing order the numerical examples illustrate the effectiveness of the derived result

the fluctuation dissipation theorem in the framework of the tsallis statistics in the framework of a generalized statistical mechanics introduced recently by tsallis 1993 we derive a generalized form of the fluctuation dissipation theorem which expresses a relation between extended susceptibilities and equilibrium fluctuations to achieve this we consistently propose a generalized functional form for the instantaneous distribution function the present theorem recovers as particular cases the corresponding generalized relations already obtained for the specific heat in terms of the generalized energy fluctuations and for the susceptibility of a magnetic system under the action of a uniform magnetic field

error bounds for the linear complementarity problem with a σ sdd matrix abstract we give new error bounds for the linear complementarity problem when the involved matrix is a sdd matrix with positive diagonals the new bounds can improve considerably other previous bounds we also find a subclass of sdd matrices for which the new bound is very simple

noncommuting multidimensional realization theory minimality reachability and observability a generalization of the notions of minimality reachability and observability for parameter dependent and multidimensional systems modeled by linear fractional transformations over noncommuting operators is presented the multidimensional system results developed herein are formally similar to and directly specialize to the standard results when one dimensional systems are considered

on an alternative to gerschgorin circles and ovals of cassini an alternative to gerschgorin circles for the localization of the real eigenvalues of a real matrix was studied in 8 in this paper we present a similar alternative to the brauer s theorem on ovals of cassini

euclidean norm estimates of the inverse of some special block matrices in this paper we start from the known lower bounds for minimal singular value of the matrices possessing certain kind of the diagonal dominance property and derive euclidean norm estimates of the inverses of several new subclasses of the block h matrices the motivation comes from applications where the matrix in question has distinguished block structure which can be exploited to obtain useful information an example arising from ecological modeling illustrates the benefits of the presented approach

estimates for bounds of some numerical characters of matrices abstract in this paper we present some new estimates on i i 2 where i is an eigenvalue of a matrix which improve schur s inequality by using these estimates we provide a new criterion for nonsingularity of matrices and a monotonic iterative method for matrix 1 balancing problems

simple criteria for nonsingular h matrices in this paper several new simple criteria for nonsingular h matrices are obtained by making use of elements of matrices only advantages are illustrated by numerical examples and a necessary condition for nonsingular h matrices is also presented

a geometric approach for reachability and observability of linear switched impulsive systems abstract this paper is concerned with the reachability and observability of linear switched impulsive systems with singular impulse matrices first some new concepts with respect to the reachability and unobservability are introduced especially span reachability is proposed because the reachable sets of switched impulsive systems do not always constitute subspaces then the geometric characterization of the span reachable and unobservable sets is presented moreover the relations between the span reachable set unobservable set and the invariant subspaces of such systems are discussed finally corresponding criteria applied to linear impulsive systems and linear switched systems are also discussed

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

common eigenvector approach to exact order reduction for roesser state space models of multidimensional systems abstract the well known popov belevitch hautus pbh tests play an important role in the kalman decomposition of 1 d systems and reveal the relationship among the eigenvalues the eigenvectors and the reducibility of a given 1 d state space model this paper is to try to generalize the pbh tests to the n d case for the exact reducibility of n d roesser models by exploiting the so called common eigenvectors specifically the notion of constrained common eigenvectors is introduced for the first time which provides insight into the relationship between reducibility and multiple eigenvalues based on this result new reducibility conditions and the corresponding reduction procedure are developed for n d roesser models it will be shown that this common eigenvector approach is applicable to a larger class of roesser models for which the existing approaches may not be applied to do further order reduction a grobner basis approach is proposed to compute such a constrained common eigenvector which also leads to an equivalent reducibility condition moreover a generalization to the state delay case is also given so that the eigenvalues of both the system matrix and the state delay system matrix can be treated simultaneously

some properties on schur complements of h matrices and diagonally dominant matrices in this paper we obtain a theorem on the distribution of eigenvalues for schur complements of h matrices further we give some properties of diagonal schur complements on diagonally dominant matrices and their distribution of eigenvalues

is a cn n a general h matrix abstract h matrices play an important role in the theory and applications of numerical linear algebra so it is very useful to know whether a given matrix a c n n usually the coefficient of a complex linear system of algebraic equations or of a linear complementarity problem a r n n with a ii 0 for i 1 2 n in this case is an h matrix then most of the classical iterative methods for the solution of the problem at hand converge in recent years the set of h matrices has been extended to what is now known as the set of general h matrices and a partition of this set in three different classes has been made the main objective of this work is to develop an algorithm that will determine the h matrix character and will identify the class to which a given matrix a c n n belongs in addition some results on the classes of general h matrices and a partition of the non h matrix set are presented

eventually sdd matrices and eigenvalue localization several classes of eventually strictly diagonally dominant matrices are introduced they are formed by nonsingular matrices and they are applied to eigenvalue localization and max norm estimation for the inverse of a given matrix

error bounds for linear complementarity problems of s nekrasov matrices and b s nekrasov matrices abstract an error bound involving a parameter which does not always work for the linear complementarity problem lcp when the involved matrices are s nekrasov matrices is provided by m garcia esnaola and j m pena 2014 in this paper a new error bound for the lcp of s nekrasov matrices is presented which depends only on the entries of the involved s nekrasov matrices based on the obtained results we also give an error bound for the lcp of b s nekrasov matrices

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

entropy evolution in self organization process h theorem and s theorem abstract the boltzmann gibbs entropy is used as a measure of the degree of order or degree of chaoticity of states of different open systems for a set of stationary states corresponding to different values of the control parameter the renormalized to a given value of the mean effective hamiltonian entropy decreases for the processes of self organization this statement was called by yu l klimontovich pis ma zh tekh fiz 9 1983 1412 the s theorem

robust stability with time varying structured uncertainty considers the problem of assessing robust stability in the presence of block diagonally structured time varying dynamic uncertainty it is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition the notion of stability here is finite gain stability over finite energy signals in sharp contrast to the case of time invariant dynamic uncertainty this result is not limited by the number uncertainty blocks these results parallel previous results regarding finite gain stability over persistent bounded signals

the schur complements of γ diagonally and product γ diagonally dominant matrix and their disc separation in this paper we obtain some estimates for the diagonally and product diagonally dominant degree of the schur complement of matrices as application we present some bounds for the eigenvalues of schur complement by the entries of the original matrix based on these results we give a kind of iteration called the schur based iteration which can solve large scale linear systems though reducing the order by the schur complement and can compute out the results faster

max norm bounds for the inverse of s nekrasov matrices max norm bounds of the inverse of an h matrix appear in a wide range of applications motivated by this fact we will start with some preliminary estimations already obtained for s sdd matrices and present new applicable and practical bounds for a wider class of s nekrasov matrices then we will comment how the scaling technique proves that new bounds improve the known ones for nekrasov matrices finally we will illustrate new results by numerical examples

multiscale analysis of information correlations in an infinite range ferromagnetic ising system the scale specific information content of the infinite range ferromagnetic ising model is examined by means of information theoretic measures of high order correlations in finite sized systems the order disorder transition region can be identified through the appearance of collective order in the ferromagnetic phase in addition it is found that near the transition the ferromagnetic phase is marked by characteristic information oscillations at scales comparable to the system size the amplitude of these oscillations increases with the total number of spins so that large scale information measures of correlations are nonanalytic in the thermodynamic limit in contrast correlations at scales small relative to the system size have a monotonic behavior both above and below the transition point and a well defined thermodynamic limit

generalizing eigenvalue theorems to pseudospectra theorems analysis of nonsymmetric matrix iterations based on eigenvalues can be misleading in this paper we discuss sixteen theorems involving varepsilon def lam lambda def lam lambda pseudospectra that each generalize a familiar eigenvalue theorem and may provide more descriptive information in some cases our organizing principle is that each pseudospectral theorem reduces precisely to the corresponding eigenvalue theorem when varepsilon def lam lambda def lam lambda 0

some remarks on a theorem of gudkov abstract we survey a nonsingularity criterion due to gudkov firstly adopting beauwens s concept of semistrict diagonal dominance we modify the criterion in order to cover a class of matrices larger than the class covered originally secondly we exploit gudkov s theorem for bounding an isolated eigenvalue and investigating the structure of the corresponding eigenvector

irreversible processes the generalized affinities within tsallis statistics abstract within the generalized statistical mechanics introduced recently by tsallis the generalized form of the affinities the quantities which drive a process in the theory of irreversible thermodynamics was derived the affinities were obtained by considering changes in the generalized entropy s q aub of a system composed by two subsystems a and b the non extensive character of the tsallis entropy is taken into account at the end the equilibrium condition is discussed and the zeroth law in the framework of the generalized thermodynamics is consistently recovered as in the usual case two systems which are in equilibrium with a third one are necessarily in equilibrium among them and share the same temperature

theorems on m splittings of a singular m matrix which depend on graph structure abstract let a m ne r n n be a splitting we investigate the spectral properties of the iteration matrix m 1n by considering the relationships of the graphs of a m n and m 1n we call a splitting an m splitting if m is a nonsingular m matrix and n 0 for an m splitting of an irreducible z matrix a we prove that the circuit index of m 1n is the greatest common divisor of certain sets of integers associated with the circuits of a for m splittings of a reducible singular m matrix we show that the spectral radius of the iteration matrix is 1 and that its multiplicity and index are independent of the splitting these results hold under somewhat weaker assumptions

exact calculation of the multiloop stability margin a mapping theorem by l a zadeh and c a desoer 1963 serves as the basis for an algorithm that computes the stability margin k sub m of diagonally perturbed multivariable feedback systems without conservatism the stability margin determination not only verifies system stability but also quantifies how much further the plan uncertainties can be extended before instability occurs the essence of the computational approach is the realization that the true image of a given domain can be approximated with arbitrary accuracy by first subdividing the domain into the requisite number of subdomains and then forming the union of the convex hulls of their images the technique is illustrated in an example with a plant model having three uncertainties in general the method is applicable to either siso or mimo lti systems whose uncertainties can be modeled with noninteracting coefficients in the open loop transfer function representations

a class of parallel decomposition type relaxation methods for large sparse systems of linear equations abstract a class of parallel decomposition type accelerated over relaxation methods including four arbitrary parameters and suitable to the simd systems is established for solving the large sparse systems of linear equations in this paper and sufficient conditions ensuring its convergence are deduced when the coefficient matrices of the linear systems of equations are respectively l matrices h matrices and positive definite matrices in particular we investigate in detail the symmetric versions of these new methods and deduce a series of conveniently applicable conditions for determining the convergence of hese versions when the coefficient matrices of the linear systems of equations are symmetric positive definite matrices

criteria for generalized diagonally dominant matrices and m matrices abstract we provide new necessary and sufficient conditions for verifying strictly generalized diagonally dominant matrices by applying the inverse of a partitioned matrix and obtain some criteria for identifying nonsingular m matrices

equivalent realizations for uncertain systems with an iqc uncertainty description this paper considers uncertain systems in terms of their corresponding system input output behavior the paper develops a necessary and sufficient condition for the input output behavior of a given uncertain system to be contained in the input output behavior of another uncertain system this result also enables one to consider the equivalence between two uncertain systems the uncertain systems under consideration are linear time varying uncertain systems in which the uncertainty is described by a time domain integral quadratic constraint

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

scaling technique for partition nekrasov matrices it is well known that for a given h matrix a there exists a diagonal nonsingular matrix that scales a by multiplying it from the right to a strictly diagonally dominant sdd matrix there are subclasses of h matrices that can be fully characterised by the form of the corresponding diagonal scaling matrices however for some applications it is not necessary to have such full characterisation it is sufficient to find at least one scaling matrix that will do the job the aim of this paper is to present a way of constructing a diagonal scaling matrix for one special subclass of h matrices called partition nekrasov matrices as an application of this scaling approach we obtain eigenvalue localisation for the corresponding schur complement matrix using only the entries of the original matrix

a comparison of error bounds for linear complementarity problems of h matrices we give new error bounds for the linear complementarity problem when the involved matrix is an h matrix with positive diagonals we find classes of h matrices for which the new bounds improve considerably other previous bounds we also show advantages of these new bounds with respect the computational cost a new perturbation bound of h matrices linear complementarity problems is also presented

application of generalized diagonal dominance in wireless sensor network optimization problems abstract the recent application of the diagonal dominance in the development of the optimization algorithms in the wireless sensor networks design has been done by yuan and yu 2006 14 extended in yu et al 2006 9 and surveyed in machado and tekinay 11 in this paper we will use the concept of generalized diagonal dominance to improve the obtained results regarding the power control game in three directions we also discuss the applicability of such improvements

a new subclass of h matrices class of h matrices plays an important role in various scientific disciplines in economics for example however this class could be used in order to get various benefits in other linear algebra fields like determinant estimation perron root estimation eigenvalue localization improvement of convergence area of relaxation methods etc for that reason it seems important to find a subclass of h matrices as wide as possible and expressed by explicit conditions involving matrix elements only one step forward in this direction starting from gudkov matrices from one side and s sdd matrices from the other side will be presented in this paper

the schur complement of strictly doubly diagonally dominant matrices and its application it is known that the schur complements of doubly diagonally dominant matrices are doubly diagonally dominant in this paper we obtain an estimate for the doubly diagonally dominant degree on the schur complement of strictly doubly diagonally dominant matrices then as an application we obtain that the eigenvalues of the schur complements are located in the brauer ovals of cassini of the original matrices under certain conditions as another application we obtain an upper bound for the infinity norm on the inverse on the schur complement of strictly doubly diagonally dominant matrices further based on the derived results we give a kind of iteration called the schur based iteration which can solve large scale linear systems though reducing the order by the schur complement and can compute out the results faster

bounds for the infinity norm of the inverse for certain m and h matrices abstract the paper presents new two sided bounds for the infinity norm of the inverse for the so called pm matrices which form a subclass of the class of nonsingular m matrices and contain the class of strictly diagonally dominant matrices these bounds are shown to be monotone with respect to the underlying partitioning of the index set and the equality cases are analyzed also an upper bound for the infinity norm of the inverse of a ph matrix whose comparison matrix is a pm matrix is derived the known ostrowski ahlberg nilson varah and moraca bounds are shown to be special cases of the upper bound obtained

a necessary and sufficient minimality condition for uncertain systems a necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations lfts on structured operator sets this condition is based on the existence of a rank deficient solution to either of a pair of linear matrix inequalities which generalize lyapunov equations the notion of gramians is thus also generalized to uncertain systems as well as kalman like decomposition structures a related minimality condition the converse of the reducibility condition may then be inferred from these results and the equivalence class of all minimal lft realizations defined these results comprise the first stage of a complete generalization of realization theory concepts to uncertain systems subsequent results such as the definition of and rank tests on structured controllability and observability matrices are also given the minimality results described are applicable to multidimensional system realizations as well as to uncertain systems connections to formal powers series representations also exist

a note on generalized diagonally dominant matrices abstract we obtain a sufficient condition for generalized diagonally dominant matrices under the assumption that a cn n is weakly diagonally dominant an equivalent condition for a to be a generalized diagonally dominant matrix is proved