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

fuzzy portfolio optimization under downside risk measures this paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return we assume that the rates of returns on securities are approximated as lr fuzzy numbers of the same shape and that the expected return and risk are evaluated by interval valued means we establish the relationship between those mean interval definitions for a given fuzzy portfolio by using suitable ordering relations finally we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form

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

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

theories of causal ordering abstract this paper is a response to iwasaki and simon 14 which criticizes de kleer and brown 8 we argue that many of their criticisms particularly concerning causality modeling and stability originate from the difference of concerns between engineering and economics our notion of causality arises from considering the interconnections of components not equations when no feedback is present the ordering produced by our qualitative physics is similar to theirs however when feedback is present our qualitative physics determines a causal ordering around feedback loops as well causal ordering is a general technique not only applicable to qualitative reasoning therefore we also explore the relationship between causal ordering and propagation of constraints upon which the methods of qualitative physics are based

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

improved error bounds based on α m for the linear complementarity problem abstract in this paper the error bounds of the approximate solution and the bounds of the true solution to the linear complementarity problem lcp m q are presented based on the function m which is introduced by mathias and pang in 23 in order to show the accuracy and the effectiveness of our results we perform some numerical experiments to reveal our results are better than other results in the literature

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

a cutting plane algorithm for mv portfolio selection model this paper deals with a portfolio selection problem with fuzzy return rates a possibilistic mean variance fmvc portfolio selection model was proposed the possibilistic programming problem can be transformed into a linear optimal problem with an additional quadratic constraint by possibilistic theory for such problems there are no special standard algorithms we propose a cutting plane algorithm to solve fmvc the nonlinear programming problem can be solved by sequence linear programming problem a numerical example is given to illustrate the behavior of the proposed model and algorithm

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

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

the composition and validation of heterogeneous control laws we present a method for creating and validating a nonlinear controller by the composition of heterogeneous local control laws appropriate to different operating regions like fuzzy logic control these methods apply even in the presence of incomplete knowledge of the structure of the system the boundaries of the operating regions or even the control action to take unlike fuzzy logic control these methods can be analyzed by a combination of classical and qualitative methods each operating region of the system has a classical control law which provides high resolution control and can be analyzed by classical methods operating regions are defined by fuzzy set membership functions the global control law is the weighted average of the local control laws where the weights are provided by the operating region membership functions a heterogeneous control law can be analyzed even in the presence of incomplete knowledge by representing it as a qualitative differential equation and using qualitative simulation to predict the set of possible behaviors of the system by expressing the desired guarantee as a statement in a modal temporal logic the validity of the guarantee can be automatically checked against the set of possible behaviors we demonstrate heterogeneous controllers and our qualitative methods for proving their properties first for a simple level controller for a water tank and second for a highly nonlinear chemical reactor

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

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

selecting the optimum portfolio using fuzzy compromise programming and sharpe s single index model different approaches besides the traditional markowitz s model have been proposed in the literature to analyze portfolio selection problems among them compromise programming cp is a suitable multiobjective programming technique which allows the handling of several objectives in those situations in which the existence of a high level of conflict between criteria does not permit the simultaneous optimization of all the considered objectives when objectives and constraints are in an imprecise environment fuzzy cp arises as a suitable solving method imprecision will be quantified by means of fuzzy numbers that represent the continuous possibility distributions for fuzzy parameters and hence place a constraint on the possible values the parameters may assume in this paper a new fuzzy compromise programming approach is proposed based on the obtaining of the minimum fuzzy distance to the fuzzy ideal solution of the portfolio selection problem once this fuzzy distance has been obtained the second step consists of finding a crisp decision vector an optimal portfolio implying a fuzzy distance to the ideal solution the more accurate as possible to the fuzzy minimum distance previously obtained

a note on a brauer s theorem abstract let a be an n n irreducible matrix and be an eigenvalue of a we obtain some necessary and sufficient conditions for to be a boundary point of the cassini oval inclusion region of the eigenvalues of a these results correct a classical result of a brauer

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

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

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

an iterative criterion for h matrices we provide an algorithmic characterization of h matrices when a is an h matrix this algorithm determines a positive diagonal matrix d such that ad is strictly row diagonally dominant in effect d is produced iteratively by quantifying and

entrywise perturbation theory for diagonally dominant m matrices with applications this paper introduces a new perspective on the study of computational problems related to diagonally dominant m matrices by establishing some new entrywise perturbation results if a diagonally dominant m matrix is perturbed in a way that each off diagonal entry and its row sums i e the quantities of diagonal dominance have small relative errors we show that its determinant cofactors each entry of the inverse and the smallest eigenvalue all have small relative errors the error bounds are given and they do not depend on any condition number applying this result to the studies of electrical circuits and tail probabilities of a queue whose embedded markov chains is of gi m 1 type we discuss the relative sensitivity of the operating speed of circuits and of the percentile of the queue length respectively

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

global qualitative description of a class of nonlinear dynamical systems in this paper we propose a methodology to derive a qualitative description of the behavior of a system from an incompletely known nonlinear dynamical model the model is written as an algebraic structure with unknown parameters and or functions under some hypotheses we obtain a graph describing the possible transitions between regions defined by the trends of the state variables and their relative positions a qualitative simulation of the model can be compared with on line data for fault detection purpose we give the example of a nonlinear biological model in dimension three for the growth of cells in a bioreactor

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

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

fuzzy compromise programming for portfolio selection the aim of this paper is to solve a portfolio selection problem using sharpe s single index model in a soft framework estimations of subjective or imprecise future beta for every asset can be represented through fuzzy numbers constructed on the basis of statistical data and the relevant knowledge of the financial analyst the model therefore works with data that contain more information than any classical model and dealing with it does not involve a great extra computational effort in order to solve the portfolio selection problem we have formulated a fuzzy compromise programming problem for this task we have introduced the fuzzy ideal solution concept based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their a cuts the accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and using discrepancy between fuzzy numbers in our analysis a major feature of this model is its sensitivity to the analyst s opinion as well as to the decision maker s preferences this allows interaction with both when it comes to design the best portfolio

portfolio selection based on upper and lower exponential possibility distributions in this paper two kinds of possibility distributions namely upper and lower possibility distributions are identified to reflect experts knowledge in portfolio selection problems portfolio selection models based on these two kinds of distributions are formulated by quadratic programming problems it can be said that a portfolio return based on the lower possibility distribution has smaller possibility spread than the one on the upper possibility distribution in addition a possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower possibility distributions to reflect the uncertainty in real investment problems a numerical example of a portfolio selection problem is given to illustrate our proposed approaches

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

some classes of nonsingular matrices and applications abstract motivated by conditions that arise from results on mean first passage times matrices in markov chains we consider here two classes of real matrices whose elements satisfy some of these conditions or variation thereof and which result in the nonsingularity of their elements the conditions are quite distinct from gersgorin circles type conditions our results lead to a sufficient condition for matrices to have 1 as their unique positive eigenvalue

mb tensors and mb0 tensors abstract the class of mb mb 0 tensors which is a generation of b b 0 tensors and quasi double b b 0 tensors is proposed and we prove that an even order symmetric mb mb 0 tensor is positive semi definite by giving some conditions to determine mb mb 0 tensors some checkable sufficient conditions for the positive semi definiteness of tensors are given

some results on b matrices and doubly b matrices abstract a real matrix with positive row sums and all its off diagonal elements bounded above by their corresponding row means was called in 4 a b matrix in 5 the class of doubly b matrices was introduced as a generalization of the previous class we present several characterizations and properties of these matrices and for the class of b matrices we consider corresponding questions for subdirect sums of two matrices a general sum of matrices introduced in 1 by s m fallat and c r johnson of which the direct sum and ordinary sum are special cases for the hadamard product of two matrices and for the kronecker product and sum of two matrices

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

an even order symmetric b tensor is positive definite it is easily checkable if a given tensor is a b tensor or a b0 tensor or not in this paper we show that a symmetric b tensor can always be decomposed to the sum of a strictly diagonally dominated symmetric m tensor and several positive multiples of partially all one tensors and a symmetric b0 tensor can always be decomposed to the sum of a diagonally dominated symmetric m tensor and several positive multiples of partially all one tensors when the order is even this implies that the corresponding b tensor is positive definite and the corresponding b0 tensor is positive semi definite this gives a checkable sufficient condition for positive definite and semi definite tensors this approach is different from the approach in the literature for proving a symmetric b matrix is positive definite as that matrix approach cannot be extended to the tensor case

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

solving a multiobjective possibilistic problem through compromise programming abstract real decision problems usually consider several objectives that have parameters which are often given by the decision maker in an imprecise way it is possible to handle these kinds of problems through multiple criteria models in terms of possibility theory here we propose a method for solving these kinds of models through a fuzzy compromise programming approach to formulate a fuzzy compromise programming problem from a possibilistic multiobjective linear programming problem the fuzzy ideal solution concept is introduced this concept is based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their cuts the accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and a definition of discrepancy between intervals is introduced in our analysis

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

solving stiff differential equations with the method of patches we introduce a new method for solving very stiff sets of ordinary differential equations the basic idea is to replace the original nonlinear equations with a set of equally stiff equations that are piecewise linear and therefore can be solved exactly we demonstrate the value of the method on small systems of equations for which some other methods are inefficient or produce spurious solutions estimate error bounds and discuss extensions of the method to larger systems of equations and to partial differential equations

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

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

a new criterion for the h matrix property for many applications it is very useful to know whether a matrix is an h matrix or not recently some iterative tests have been proposed for distinguishing h matrix in this paper we propose a new method for being able to distinguish only a scalar times column vector numerical evidence for the effectiveness of the proposed algorithm is presented

fuzzy mean variance skewness portfolio selection models by interval analysis in portfolio selection problem the expected return risk liquidity etc cannot be predicted precisely the investor generally makes his portfolio decision according to his experience and his economic wisdom so deterministic portfolio selection is not a good choice for the investor in most of the recent works on this problem fuzzy set theory is widely used to model the problem in uncertain environments this paper utilizes the concept of interval numbers in fuzzy set theory to extend the classical mean variance mv portfolio selection model into mean variance skewness mvs model with consideration of transaction cost in addition some other criteria like short and long term returns liquidity dividends number of assets in the portfolio and the maximum and minimum allowable capital invested in stocks of any selected company are considered three different models have been proposed by defining the future financial market optimistically pessimistically and in the combined form to model the fuzzy mvs portfolio selection problem in order to solve the models fuzzy simulation fs and elitist genetic algorithm ega are integrated to produce a more powerful and effective hybrid intelligence algorithm hia finally our approaches are tested on a set of stock data from bombay stock exchange bse

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

on a class of nonsingular matrices containing b matrices abstract a real matrix with positive row sums and all its off diagonal elements bounded above by their corresponding row means was called in 12 a b matrix the classes of doubly b matrices and of b r matrices were introduced in 13 and 11 as generalizations of the previous class we present characterizations and properties of b r matrices and we consider the problem of when a subdirect sum of two matrices in this class lies in the same class

causality in device behavior abstract this paper shows how formal characterizations of causality and of the method of comparative statics long used in econometrics thermodynamics and other domains can be applied to clarify and make rigorous the qualitative causal calculus recently proposed by de kleer and brown 2 the formalization shows exactly what assumptions are required to carry out causal analysis of a system of interdependent variables in equilibrium and to propagate disturbances through such a system the intuitive concepts of causality captured by de kleer and brown provide a rough approximation to the standard analytic techniques that are used in the treatment of simultaneous algebraic and differential equations

a dynamic systems perspective on qualitative simulation abstract this paper presents a simple geometric interpretation of qualitative simulation qs based on the phase space representation of dynamic systems theory qs consists of two steps transition analysis determines the sequence of qualitative states that a system traverses and global interpretation derives its long term behavior i recast transition analysis as a search problem in phase space and replace the assorted transition rules with two algebraic conditions the first condition determines transitions between arbitrarily shaped regions in phase space as opposed to qs which only handles n dimensional rectangles it also provides more accurate results by considering only the boundaries between regions the second condition determines whether nearby trajectories approach a fixed point asymptotically it obtains better results than qs by exploiting local stability properties i recast global interpretation of dissipative systems as a search for attractors in phase space and present a global interpretation strategy for the subset of these systems whose local behavior determines global behavior uniquely although limited in scope this strategy handles many systems that appear in the qs literature

some classes of nonsingular matrices with applications to localize the real eigenvalues of real matrices abstract we first present some classes of nonsingular matrices which are then applied to give some simple nonsingular criteria inclusion and exclusion regions of real eigenvalues for real matrices in particular the real eigenvalues different from 1 of any stochastic matrix are localized more precisely

automatic analysis of one parameter planar ordinary differential equations by intelligent numeric simulation abstract this paper describes research on automating the analysis of physical systems modeled by ordinary differential equations it describes a program called poincare that analyzes one parameter autonomous planar systems at the level of experts through a combination of theoretical dynamics numerical simulation and geometric reasoning the input is the system a bounding box for the system state a bounding interval for the parameter and error tolerances poincare partitions the parameter interval into open subintervals of equivalent behavior bounded by bifurcation points classifies the bifurcation points and constructs representative phase diagrams for the subintervals it detects local and global generic one parameter bifurcations it constructs the phase diagrams by identifying fixed points saddle manifolds and limit cycles and partitioning the remaining trajectories into open regions of uniform asymptotic behavior it obtains the region boundaries by numeric simulation guided by theoretical knowledge it determines the behavior near fixed points from the jacobian of the system scans outward to find basins of attractors and limit cycles and stops at the bounding box

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

automatic qualitative analysis of dynamic systems using piecewise linear approximations abstract this paper explores automating the qualitative analysis of physical systems it describes a program called plr for piecewise linear reasoner that formalizes an analysis strategy employed by experts plr takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values it approximates intractable nonlinear systems with piecewise linear ones analyzes the approximations and draws conclusions about the original systems it chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes yet simple enough to be analyzed completely and efficiently it derives additional properties such as boundedness or periodicity by theoretical methods plr s analysis depends on abstract properties of systems rather than on specific numeric values this makes its conclusions more robust and enables it to handle parameterized equations transparently i demonstrate plr on several common nonlinear systems and on published examples from mechanical engineering

chaos in a three dimensional single loop feedback system with a piecewice linear feedbackk function abstract this paper describes chaotic behaviour in a single loop feedback system of low order the system is particularly simple and because it is piecewise linear and hence can be undersdtood globally a description of the flow much more complete than usual can be given an orbit structure is suggested for the system after a minor approximation is considered the approximation gives two equivalent discrete one dimensional maps of the interval to itself and these maps are discussed in the light of recent work the validity of the approximation is confirmed by computer simulation

portfolio selection based on fuzzy cross entropy in this paper the kapur cross entropy minimization model for portfolio selection problem is discussed under fuzzy environment which minimizes the divergence of the fuzzy investment return from a priori one first three mathematical models are proposed by defining divergence as cross entropy average return as expected value and risk as variance semivariance and chance of bad outcome respectively in order to solve these models under fuzzy environment a hybrid intelligent algorithm is designed by integrating numerical integration fuzzy simulation and genetic algorithm finally several numerical examples are given to illustrate the modeling idea and the effectiveness of the proposed algorithm

mean semivariance models for fuzzy portfolio selection this paper discusses portfolio selection problem in fuzzy environment in the paper semivariance is originally presented for fuzzy variable and three properties of the semivariance are proven based on the concept of semivariance of fuzzy variable two fuzzy mean semivariance models are proposed to solve the new models in general cases a fuzzy simulation based genetic algorithm is presented in the paper in addition two numerical examples are also presented to illustrate the modelling idea and the effectiveness of the designed algorithm

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

double b tensors and quasi double b tensors abstract in this paper we propose two new classes of tensors double b tensors and quasi double b tensors give some properties of double b tensors and quasi double b tensors discuss their relationships with b tensors and positive definite tensors and show that even order symmetric double b tensors and even order symmetric quasi double b tensors are positive definite these give some checkable sufficient conditions for the positive definiteness of tensors

towards a practical theory of reformulation for reasoning about physical systems reformulation is ubiquitous in problem solving and is especially common in modeling physical systems in this paper we examine reformulation techniques in the context of reasoning about physical systems this paper does not present a general theory of reformulation but it studies a number of known reformulation techniques to achieve a broad understanding of the space of available reformulations in doing so we present a practical framework for specifying classifying and evaluating various reformulation techniques applicable to this class of problems our framework provides the terminology to specify the conditions under which a particular reformulation technique is applicable the cost associated with performing the reformulation and the effects of the reformulation with respect to the problem encoding

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

doubly diagonally dominant matrices we consider the class of doubly diagonally dominant matrices a ajj e c la 1 l jjl ck i laiklck jlajkl i j and its subclasses we give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an h matrix as in the case of diagonal dominance we show that the schur complements of doubly diagonally dominant matrices inherit this property moreover we describe when a schur complement of a strictly doubly diagonally dominant matrix is strictly diagonally dominant 0 elsevier science inc 1997 1 preliminaries

mean variance skewness model for portfolio selection with fuzzy returns numerous empirical studies show that portfolio returns are generally asymmetric and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same in order to measure the asymmetry of fuzzy portfolio return a concept of skewness is defined as the third central moment in this paper and its mathematical properties are studied as an extension of the fuzzy mean variance model a mean variance skewness model is presented and the corresponding variations are also considered in order to solve the proposed models a genetic algorithm integrating fuzzy simulation is designed finally several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm

ill conditioned matrices are componentwise near to singularity for a square matrix normed to 1 the normwise distance to singularity is well known to be equal to the reciprocal of the condition number in this paper we give an elementary and self contained proof for the fact that an ill conditioned matrix is also not far from a singular matrix in a componentwise sense this is shown to be true for any weighting of the componentwise distance in other words for matrix inversion ill conditioned means nearly ill posed in the normwise and also in the componentwise sense

a linear complementarity problem with a p matrix in this paper we present an application of a linear complementarity problem where m is a p matrix but in general is neither an h matrix nor a positive definite matrix this application occurs originally in j rohn linear algebra appl 126 1989 pp 39 78 which is less known to the lcp community its focus is in computing the exact interval enclosures of the components of the solution set of an interval linear system we extend the idea such that the calculations can be done by a computer with rigorous error control

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

solving the multiobjective possibilistic linear programming problem in conventional multiobjective decision making problems the estimation of the parameters of the model is often a problematic task normally they are either given by the decision maker dm who has imprecise information and or expresses his considerations subjectively or by statistical inference from past data and their stability is doubtful therefore it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets for which a lot of fuzzy approaches to multiobjective programming have been developed in this paper we propose a method to solve a multiobjective linear programming problem involving fuzzy parameters fp molp whose possibility distributions are given by fuzzy numbers estimated from the information provided by the dm as the parameters intervening in the model are fuzzy the solutions will be also fuzzy we propose a new pareto optimal solution concept for fuzzy multiobjective programming problems it is based on the extension principle and the joint possibility distribution of the fuzzy parameters of the problem the method relies on cuts of the fuzzy solution to generate its possibility distributions these ideas are illustrated with a numerical example

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

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

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

the expected value of a fuzzy number abstract the notions of expected interval and expected value of fuzzy number are introduced the expected interval is defined as the expected value of an interval random set generated by the fuzzy number and the expected value of this number is defined as the centre of the expected interval the linearity of the expected interval is studied

accurate computation of the smallest eigenvalue of a diagonally dominant m matrix if each off diagonal entry and the sum of each row of a diagonally dominant m matrix are known to certain relative accuracy then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers in this paper we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms

some remarks on p p0 b and b0 tensors abstract recently song and qi extended the concept of p p 0 and b matrices to p p 0 b and b 0 tensors obtained some properties about these tensors and proposed many questions for further research in this paper we answer three questions mentioned as above and obtain further results about p p 0 b and b 0 tensors

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