comments on perturbation bounds for root clustering of linear systems in a specified second order subregion this paper comments on the results of the above mentioned paper by bakker luo johnson ibid vol 40 1995 we note that theorems 3 1 and 4 1 are incorrectly stated i e they are not valid for the non spl omega transformable regions the results cannot cover the ride quality region listed in table 1 since it is a non spl omega transformable region

ten methods to bound multiple roots of polynomials given a univariate polynomial p with a k fold multiple root or a k fold root cluster near some z we discuss nine different methods to compute a disc near z which either contains exactly or contains at least k roots of p many of the presented methods are known some are new we are especially interested in the behaviour of methods when implemented in a rigorous way that is when taking into account all possible effects of rounding errors in other words every result shall be mathematically correct we display extensive test sets comparing the methods under different circumstances based on the results we present a tenth a hybrid method combining five of the previous methods which for given z i detects the number k of roots near z and ii computes an including disc with in most cases a radius of the order of the numerical sensitivity of the root cluster therefore the resulting discs are numerically nearly optimal

on the performance advantage of multitaper spectral analysis the performance advantage of multitaper spectral analysis is quantified relative to weighted overlapped segment averaging wosa to make the comparison of these two nonparametric spectral estimators theoretical performance measures are derived in terms of leakage variance and resolution the methods are then compared by evaluating each measure in turn while requiring the other two measures to be equal the results show that multitaper analysis always performs better than wosa for example given the same leakage and resolution multitaper analysis can have three quarters to one half the variance of wosa given the same resolution and variance multitaper analysis can exhibit a 10 20 db leakage advantage over wosa these and other results provide compelling evidence for greater use of multitaper analysis in situations for which a nonparametric spectral estimator is appropriate

on homogeneous and self dual algorithms for lcp we present some generalizations of a homogeneous and self dual linear programming lp algorithm to solving the monotone linear complementarity problem lcp again while it achieves the best known interior point iteration complexity the algorithm does not need to use any big m number and it detects lcp infeasibility by generating a certificate to our knowledge this is the first interior point and infeasible starting algorithm for the lcp with these desired features

numerical validation of solutions of complementarity the nonlinear case this paper proposes a validation method for solutions of nonlinear complementarity problems the validation procedure performs a computational test if the result of the test is positive then it is guaranteed that a given multi dimensional interval either includes a solution or excludes all solutions of the nonlinear complementarity problem

computing gaussian likelihoods and their derivatives for general linear mixed models algorithms are described for computing the gaussian likelihood or restricted likelihood corresponding to a general linear mixed model included are arbitrary covariance structures for both the random effects and errors formulas are also given for the first and second derivatives of the likelihoods thus enabling a newton raphson implementation the algorithms make heavy use of the cholesky decomposition the sweep operator and the w transformation also described are the modifications needed for variance profiling fisher scoring and mivque 0 as well as the computational order of the procedures

multitaper estimation of the innovation variance of a stationary time series accurate computation of the innovation variance of a stationary time series by a nonparametric method provides useful information to judge the quality of fit of parametric models for the time series previous estimators of the innovation variance have made use of raw periodogram ordinates smoothed periodogram ordinates or periodogram ordinates following tapering smoothing provides more degrees of freedom at each frequency but fewer independent estimates whereas tapering reduces side lobe leakage if the dynamic range of the spectrum is high but produces only two degrees of freedom at each frequency here we investigate estimation of innovation variance from finite sample sizes by the use of multiple tapering the tapers are designed to reduce side lobe leakage and produce increased degrees of freedom at each frequency it is demonstrated that the multiple tapering approach produces much better estimates of the innovations variance than the other methods when the spectrum has a high dynamic range and or is rapidly varying the multitaper bandwidth parameter w may be selected using an obvious heuristic approach or by an automatic method the multitaper method is hence an attractive alternative to conventional techniques

multiple window cepstrum analysis for estimation of periodicity multiple windows have been used in spectrum analysis to reduce variance in this paper a multiple window approach is suggested in cepstrum analysis where the period of the system response should be estimated the logarithm of the spectrum as well as the liftering are approximated by a division of two multiple window spectra the method is useful especially in the case of short periods of the periodic signal and large spectral dynamics of the other signal i e the case with severe overlap in the cepstrum examples are given for estimation of periods of surface waves traveling around the circumference of tree trunks

on p matrices we present some necessary and sufficient conditions for a real matrix to be a p matrix they are based on the sign real spectral radius and regularity of a certain interval matrix we show that no minor can be left out when checking for p property furthermore a not necessarily exponential method for checking the p property is given

igaor and multisplitting igaor methods for linear complementarity problems in this paper we propose an interval version of the generalized accelerated overrelaxation methods which we refer to as igaor for solving the linear complementarity problems lcp m q and develop a class of multisplitting igaor methods which can be easily implemented in parallel in addition in regards to the h matrix with positive diagonal elements we prove the convergence of these algorithms and illustrate their efficiency through our numerical results

efficient numerical validation of solutions of nonlinear systems a new stopping criterion for newton s method is derived by combining the properties of the krawczyk operator and a corollary of the newton kantorovich theorem when this criterion is satisfied the authors use the last three newton iterates to compute an interval vector that is very likely to contain a solution of the given nonlinear system the existence of such a solution is tested using krawczyk s operator furthermore each element from this interval vector considered as an approximation to the solution has a relative error that is of the order of the machine precision extensive numerical testing has shown that the proposed method has very good practical performance

on the existence of an eigenvalue below the essential spectrum this paper is concerned with a computer assisted proof of eigenvalues below the essential spectrum of the sturm liouville problem on the half line it uses methods of functional analysis and interval analysis to derive algorithms that may be used to prove the existence of such eigenvalues

on positivity of principal minors of bivariate bezier collocation matrix it is well known that the bivariate polynomial interpolation problem at uniformly distributed domain points of a triangle is correct thus the corresponding interpolation matrix m is nonsingular schumaker stated the conjecture that all principal submatrices of m are nonsingular too furthermore all of the corresponding determinants the principal minors are conjectured to be positive this result would solve the constrained interpolation problem in this paper the conjecture on minors for polynomial degree 17 and conjecture for some particular configurations of domain points are confirmed

an eigenvalue approach evaluating minors for weighing matrices w n n 1 abstract in the present paper we concentrate our study on the evaluation of minors for weighing matrices w n n 1 theoretical proofs concerning their minors up to the order of n 4 n 4 are derived introducing an eigenvalue approach a general theorem specifying the analytical form of any n l n l minor is developed an application to the growth problem for weighing matrices is given

feedback nash equilibria in linear quadratic difference games with constraints in this paper we consider a class of noncooperative n player finite horizon linear quadratic dynamic games with linear constraints we introduce a constrained feedback information structure and provide necessary and sufficient conditions for the existence of a constrained feedback nash equilibrium for this class of games we show that the constrained feedback nash equilibrium can be obtained from a feedback nash equilibrium associated with an unconstrained multi parametric linear quadratic game where the parameters satisfy an equilibrium property we show that this relation leads to a fixed point interpretation further under a few additional assumptions we show that these fixed points can be obtained as solutions of a single large scale linear complementarity problem thereby providing a method to compute the constrained feedback nash equilibria we illustrate our results with a numerical example

the variance of multitaper spectrum estimates for real gaussian processes multitaper spectral estimation has proven very powerful as a spectral analysis method wherever the spectrum of interest is detailed and or varies rapidly with a large dynamic range in his original paper d j thomson 1982 gave a simple approximation for the variance of a multitaper spectral estimate which is generally adequate when the spectrum is slowly varying over the taper bandwidth the authors show that near zero or nyquist frequency this approximation is poor even for white noise and derive the exact expression of the variance in the general case of a stationary real valued time series this expression is illustrated on an autoregressive time series and a convenient computational approach outlined it is shown that this multitaper variance expression for real valued processes is not derivable as a special case of the multitaper variance for complex valued circularly symmetric processes as previously suggested in the literature

principal pivot transforms properties and applications the principal pivot transform ppt is a transformation of the matrix of a linear system tantamount to exchanging unknowns with the corresponding entries of the right hand side of the system the notion of the ppt is encountered in mathematical programming statistics and numerical analysis among other areas the purpose of this paper is to draw attention to the main properties and uses of ppts make some new observations and motivate further applications of ppts in matrix theory special consideration is given to ppts of matrices whose principal minors are positive 2000 elsevier science inc all rights reserved

sign solvable linear complementarity problems abstract this paper presents a connection between qualitative matrix theory and linear complementarity problems lcps an lcp is said to be sign solvable if the set of the sign patterns of the solutions is uniquely determined by the sign patterns of the given coefficients we provide a characterization for sign solvable lcps such that the coefficient matrix has nonzero diagonals which can be tested in polynomial time this characterization leads to an efficient combinatorial algorithm to find the sign pattern of a solution for these lcps the algorithm runs in o time where is the number of the nonzero coefficients

statistical properties for coherence estimators from evolutionary spectra evolutionary spectra were developed by priestley to extend spectral analysis to some nonstationary time series in particular semistationary processes of which the ubiquitous uniformly modulated processes are a subclass coherence is well defined for bivariate semistationary processes and can be estimated from such processes we consider priestley s estimator for the evolutionary spectral density matrix and show that its elements can be written as weighted multitaper estimators with calculable weights and tapers under gaussianity an approximating wishart distribution model follows for the spectral matrix valid for all frequencies except small computable intervals near zero and nyquist moreover the critically important degrees of freedom are known consequently the statistical distribution of the coherence is given by goodman s distribution and the raw coherence estimate can be accurately debiased theoretical results are verified using a model for wind fluctuations simulations give excellent agreement between the mean debiased coherence estimates and true coherence and between the proposed and empirical distributions of coherence

the p matrix problem is co np complete recently rohn and poljak proved that for interval matrices with rank one radius matrices testing singularity is np complete this paper will show that given any matrix family belonging to the class of matrix polytopes with hypercube domains and rank one perturbation matrices a class which contains the interval matrices testing singularity reduces to testing whether a certain matrix is not a p matrix it follows from this result that the problem of testing whether a given matrix is a p matrix is co np complete

extended p pairs abstract a p matrix is a square matrix with positive principal minors we introduce a natural extension of the class of p matrices the class of extended p pairs a pair i m for a p matrix m is shown to be contained in an extended p pair iff sms has an n step vector for some sign matrix s such a matrix m is called extendable and an example of a p matrix that is not extendable is given applications to the linear complementarity problem are discussed a polynomial time algorithm to determine if a pair of matrices is an extended p pair is given

randomized pivot algorithms for p matrix linear complementarity problems we study orientations of the n cube that come from simple principal pivot algorithms for the linear complementarity problem with a p matrix we show that these orientations properly generalize those that are obtained from linear objective functions on polytopes combinatorially equivalent to the cube the orientations from lcp with a p matrix may admit directed cycles we give a sequence of problems on which the algorithm random edge performs very badly

componentwise pseudospectrum of a matrix abstract given a nonnegative weight matrix e defining componentwise structured perturbations e e we introduce a componentwise pseudospectrum of a square matrix a as contour sets of the function c a i 1 e where m is the spectral radius of a square matrix m and discuss how to compute it

orthogonal sets of data windows constructed from trigonometric polynomials suboptimal easily computable substitutes for the discrete prolate spheroidal windows used by d j thomson proc ieee vol 70 p 1055 1096 1982 for spectral estimation are given trigonometric coefficients and energy leakages of the window polynomials are tabulated

combinatorial characterizations of k matrices abstract e present a number of combinatorial characterizations of k matrices this extends a theorem of fiedler and ptak on linear algebraic characterizations of k matrices to the setting of oriented matroids our proof is elementary and simplifies the original proof substantially by exploiting the duality of oriented matroids as an application we show that any simple principal pivot method applied to the linear complementarity problems with k matrices converges very quickly by a purely combinatorial argument

systems of linear interval equations this paper presents theory and methods for computing the exact bounds on the solution of a system of n linear equations in n variables whose coefficients and right hand sides vary in some real intervals finite and iterative methods are given based on results from linear complementarity theory also regularity conditions regularity testing and computing the exact inverse of an interval matrix are dealt with

a frequency domain approach to eigenvalue based detection with diversity reception and spectrum estimation in this paper we investigate a frequency domain approach for eigenvalue based detection of a primary user based on equal gain combining egc and spectrum estimation with bartlett s method this paper considers two techniques for eigenvalue detection which are maximum eigenvalue detection med and the maximum minimum eigenvalue mme detector we exploit the eigenvalues that are associated with the hermitian form representation of bartlett s estimate to assess the performance of the aforementioned eigenvalue techniques in the frequency domain for each case we quantify the performance based on the probabilities of false alarm and missed detection over rayleigh and rician fading a bivariate mellin transform approach is employed to obtain the probability distribution function for the ratio of the extreme eigenvalues under each hypothesis all obtained formulas are validated via monte carlo simulations and the results give a clear insight into the performance of the investigated methods in frequency domain med outperforms both the mme detector and periodogram based energy detection even in a worst case scenario of noise uncertainty while the mme detector exhibits heavy tailed statistical characteristics and thus its receiver operating characteristics tend to stay on the line of no discrimination the performance of med is further enhanced by careful choice of combinations of the total length of the sensing frame and number of sub slots

a homological characterization of q matrices a real square matrix m is said to be a q matrix if the linear complementarity problem q m has a solution for every vector q there is as yet no characterization of q matrices which makes it easy to determine whether or not a given matrix is q ideas from topology in particular degreetheory have previously been used to obtain sufficient conditions for when a matrix is q in this paper we will apply some other ideas from topology to give a homological characterization of q matrices continuing to borrow from topology we define the nerve of a matrix which along with our characterization leads to an algorithm for checking whether or not a matrix is q this algorithm has smaller bounds on its worst case time complexity than previous methods

a unified view of multitaper multivariate spectral estimation summary the orthogonal multitaper framework for cross spectral estimators provides a simple unifying structure for determining the corresponding statistical properties here crossspectral estimators are represented by a weighted average of orthogonally tapered crossperiodograms with the weights corresponding to a set of rescaled eigenvalues such a structure not only encompasses the thomson estimators using slepian and sine tapers but also welch s weighted overlapped segment averaging estimator and lag window estimators including frequency averaged cross periodograms the means smoothing and leakage biases variances and asymptotic distributions of such estimators can all be formulated in a common way comparisons are made for a fixed number of degrees of freedom the common structure of the estimators also provides a necessary condition for the invertibility of an estimated cross spectral matrix namely that the weight matrix of the estimator written in bilinear form must have rank greater than or equal to the dimension of the cross spectral matrix an example is given showing the importance of small leakage and thus illustrating that the various estimators need not be equivalent in practice

numerical validation of solutions of linear complementarity problems this paper proposes a validation method for solutions of linear complementarity problems the validation procedure consists of two sufficient conditions that can be tested on a digital computer if the first condition is satisfied then a given multidimensional interval centered at an approximate solution of the problem is guaranteed to contain an exact solution if the second condition is satisfied then the multidimensional interval is guaranteed to contain no exact solution this study is based on the mean value theorem for absolutely continuous functions and the reformulation of linear complementarity problems as nonsmooth nonlinear systems of equations

flory theory for directed lattice animals and directed percolation the free energies of directed lattice animals in good and theta solvents and the free energy of directed percolation are found by the use of a simple flory type approximation which accounts for the inherent anisotropy of these systems from these free energies the authors obtain the upper critical dimension below which mean field theory breaks down they also calculate closed form dimension dependent expressions for the parallel and perpendicular correlation length exponents which characterise the asymptotic cluster shapes these exponents are in excellent agreement with existing numerical data

the quadrifocal variety abstract multi view geometry is reviewed from an algebraic geometry perspective and multi focal tensors are constructed as equivariant projections of the grassmannian a connection to the principal minor assignment problem is made by considering several flatlander cameras the ideal of the quadrifocal variety is computed up to degree 8 and partially in degree 9 using the representations of gl 3 4 in the polynomial ring on the space of 3 3 3 3 tensors further representation theoretic analysis gives a lower bound for the number of minimal generators

self validating methods abstract we present some ideas on self validating sv methods this note is especially intended to give some background for the articles in this special volume of laa it is not intended to be a survey of the big variety of all possible aspects of sv methods but rather a summary of some basic concepts especially some common misconceptions are mentioned and explored

local discretization error bounds using interval boundary element method in this paper a method to account for the point wise discretization error in the solution for boundary element method is developed interval methods are used to enclose the boundary integral equation and a sharp parametric solver for the interval linear system of equations is presented the developed method does not assume any special properties besides the laplace equation being a linear elliptic partial differential equation whose green s function for an isotropic media is known numerical results are presented showing the guarantee of the bounds on the solution as well as the convergence of the discretization error copyright 2008 john wiley sons ltd

on the performance of energy detection using bartlett s estimate for spectrum sensing in cognitive radio systems energy detection can be used for spectrum sensing in cognitive radios when no prior knowledge about the primary signals is available the performance of this technique however is strongly influenced by the available decision estimate this paper presents accurate performance analysis of energy detection when using bartlett s estimate as a test statistic both independent and identically distributed rayleigh and rician fading channels are investigated for unknown signals with complex envelopes the novel contribution here is threefold first the quadratic form representation of bartlett s estimate is formulated then starting from the characteristic function the cumulative distribution function is derived for each type of channel and accurate expressions are developed for the probabilities of false alarm and missed detection finally a performance comparison with the raw periodogram is presented the accuracy of the proposed analysis is confirmed using monte carlo trials the results provide valuable insight into the performance of bartlett s based energy detection it will be seen that the additional degrees of freedom associated with bartlett s method empower it to offer excellent performance when compared with the raw periodogram bartlett s consistently leads to lower probability of miss but its probability of false alarm is only superior at relatively higher sensing thresholds

on spectrum sensing of ofdm signals at low snr new detectors and asymptotic performance this paper deals with near optimal spectrum sensing of orthogonal frequency division multiplexing ofdm signals to achieve reliable detection at low signal to noise ratio snr the likelihood ratio test lrt a simple hypothesis test delivers the optimal performance but it requires that the parameters involved in the test are known hence the generalized likelihood ratio test glrt a composite hypothesis test has often been employed however glrt based detectors involve biased parameter estimation which may lead to inferior performance in this paper with proper approximation the lrt is reduced to a simpler form which only requires the knowledge of noise power then a novel unbiased and consistent estimator of the noise power is developed this estimator is combined with the approximate lrt leading to an asymptotic simple hypothesis test asht two asht based detectors are presented for cases with and without time synchronization and their theoretical performances are analyzed simulation results show that the asht based detectors deliver performances very close to that of the optimal lrt and significantly outperform the existing glrt based detectors it is also shown that the asht based detectors exhibit robustness against the influence of multipath channels

an efficient algorithm for the symmetric principal minor assignment problem abstract we consider the problem of reconstructing a symmetric matrix from its principal minors which has several applications in information theory and statistical modeling we develop a theory of symmetric matrices with equal corresponding principal minors based on a simple equivalent property due to oeding 2011 10 we then use this theory to provide a method for choosing a canonical representative from the class of all symmetric matrices with specified principal minors finally we provide an efficient algorithm for computing this canonical representative given its principal minors as input

modeling and performance analysis of multitaper detection using phase type distributions over mimo fading channels this paper presents modeling and analysis of two variations of the multitaper detector namely multiple antenna detection of a single user multiple input multiple output mimo node and the multitaper method mtm combined with singular value decomposition svd which is known as the mtm svd processor motivated by the reputation of the mtm as the best nonparametric power spectral density psd estimator and after reviewing the limited previous research attempts which focus on single input single output siso multitapering we present the exact analytical models for the two considered derivatives of the multitaper method over fading channels by making use of the theory of hermitian forms and phase type distributions in addition using the neyman pearson approach npa the performance of both detectors is optimized over nakagami fading for both multitaper variations we accurately derive the eigenvalues of the hermitian form of each detector where the eigenvalues identify the phase type distribution parameters this yields generalized expressions for the probabilities of false alarm and missed detection when arbitrary multitaper weights are used finally we investigate the impact of noise uncertainty on the performance of mimo mtm the results show that performance of both detectors is dependent on the total number of discrete prolate spheriodal sequences dpsss while for the mtm svd processor the performance is also dependent on the number of cooperating users and the employed frequency resolution it is also shown that mimo mtm is robust under noise uncertainty the obtained analytical models are proven to be accurate and enables further investigations on the multitaper detector

performance analysis of the periodogram based energy detector in fading channels in this paper we provide a performance analysis of cognitive radio systems employing energy detection based on power spectral density estimation specifically we derive mathematical expressions for the probabilities of false alarm and missed detection when the periodogram estimate is used as a decision statistic first using the characteristic function of the quadratic form representation of the periodogram we study the characteristics of the product of the sample covariance matrix of the observed vector and the symmetric matrix of the quadratic form we have found that this product is rank 1 with one non zero eigenvalue and therefore a simplified expression for the cumulative density function cdf is obtained second the cdf is exploited to derive accurate mathematical expressions for the probabilities of false alarm and missed detection in both rayleigh and rician fading channels also for each case we have derived the probability distribution function pdf of the corresponding eigenvalues the results demonstrate that the probabilities of false alarm and missed detection are independent of the length of the observations when all the other parameters remain fixed the results also reveal that the considered frequency domain based energy detector is superior to its conventional time domain counterpart as it provides fewer false alarms

skew symmetric matrices and their principal minors abstract in this article we study the following problem given a positive integer k what is the relationship between two matrices with entries in a field k and having equal corresponding principal minors of order at most k our main theorem improves a result of loewy 13 for skew symmetric matrices all of whose off diagonal entries are nonzero

configurational statistics of a disordered polymer chain a problem of the configurational properties of a long flexible polymer chain with a quenched disorder is considered the chain is assumed to be randomly constructed from monomers of two different kinds with different constants for the two body interaction near the theta point i e when the average interaction of monomers is small the spatial correlation of the repulsive and attractive monomers of different kinds leads to an increase of effects of the disorder on large scales there is also the competing effect of the repulsive three body interaction which tends to screen the effects of disorder on large scales for both effects the upper critical dimension is dc 3 a solution of the renormalisation group equation indicates that there always exists a critical scale at which the relative dispersion of sizes of polymers with different random sequences of monomers becomes of the order of unity the magnitude of this critical scale depends strongly on the relation between the constant which characterises the dispersion of the two body interaction b0 and the constant of the repulsive three body interaction v0 if b0 3 32v0 at each physically attainable scale the effects of screening are prevalent and the dispersion of sizes of polymers with different sequences of monomers is small near the theta point if the reverse inequality holds the dispersion of sizes becomes of the order of unity near the theta point

hyperdeterminantal relations among symmetric principal minors abstract the principal minors of a symmetric n n matrix form a vector of length 2 n we characterize these vectors in terms of algebraic equations derived from the 2 2 2 hyperdeterminant

chaos in the lorenz equators a computer assisted proof part ii details details of a new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described the technique combines abstract existence results based on the conley index theory with rigorous computer assisted computations as an application of these methods it is proven that for some explicit parameter values the lorenz equations exhibit chaotic dynamics

optimized weighted averaging of peak matched multiple window spectrum estimators periodogram averaging with multiple windows can be used in spectrum analysis of nonstationary data usually however the windows for the subspectra are equally weighted in the estimate in this correspondence a criterion for the optimization of weighting factors is formulated as the average of normalized bias variance or mean square error in a certain frequency interval around a predefined peaked spectrum the weighting factors are optimized using the peak matched multiple windows the sinusoid multiple windows and the discrete prolate spheroidal sequences

principal minors part i a method for computing all the principal minors of a matrix an order o 2 n algorithm for computing all the principal minors of an arbitrary n n complex matrix is motivated and presented offering an improvement by a factor of n 3 over direct computation the algorithm uses recursive schur complementation and submatrix extraction storing the answer in a binary order an implementation of the algorithm in matlab is also given and practical considerations are discussed and treated accordingly

mse estimates for multitaper spectral estimation and off grid compressive sensing we obtain estimates for the mean squared error mse for the multitaper spectral estimator and certain compressive acquisition methods for multi band signals we confirm a fact discovered by thomson spectrum estimation and harmonic analysis proc ieee 1982 assuming bandwidth w and n time domain observations the average of the square of the first k lfloor 2nw rfloor slepian functions approaches as k grows an ideal bandpass kernel for the interval w w we provide an analytic proof of this fact and measure the corresponding rate of convergence in l 1 norm this validates a heuristic approximation used to control the mse of the multitaper estimator the estimates have also consequences for the method of compressive acquisition of multi band signals introduced by davenport and wakin giving mse approximation bounds for the dictionary formed by modulation of the critical number of prolates

inverse m matrices abstract this is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of m matrices and is aimed at an audience conversant with basic ideas of matrix theory a theme is the parallels anddifferences between the class of m matrices and the class of inverse m matrices among the primary tools used are diagonal multiplications the neumann expansion and the form of the inverse of a partitioned matrix some of the results seem not to have appeared before and several unsolved problems are mentioned

a statistical resolution theory of the ar method of spectral analysis the autoregressive ar method of spectral analysis is widely used in diverse areas for its solid theoretical foundation interesting physical interpretation computational efficiency and more importantly high resolution capability various aspects of its statistical performance have been investigated however the resolution probability that provides the most rigorous description of the spectrum resolution capability is still not available in the literature in this paper by formulating the resolution event in the framework of statistical decision theory and directly determining its probability from its characteristic function we obtain an exact asymptotic formula for the probability of resolution on this basis we determine the limiting resolving behavior of the sample ar spectrum and develop the corresponding geometrical insight in the parametric space simulation and numerical results are also presented to confirm and illustrate the theory

box invariance in biologically inspired dynamical systems a dynamical system is box invariant if there exists a box shaped positively invariant region we show that box invariance can be checked in cubic time for linear and affine systems and that it remains decidable for classes of nonlinear systems of interest with polynomial structure we present results on the robustness of box invariance for linear systems using spectral properties of metzler matrices we also present sufficient conditions for establishing box invariance of switched and hybrid systems in general we argue that box invariance is a characteristic of many biologically inspired dynamical models

the efficiency of the flory approximation the flory approximation 1969 for the self avoiding chain problem is compared with a conventional perturbation theory expansion while in perturbation theory each term is averaged over the unperturbed set of configurations the flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations this imposes restrictions on the integration domain in higher order terms and they can be treated self consistently the accuracy delta nu nu of the flory approximation for self avoiding chain problems is estimated to be 10 1 10 2 for 1 d 4

a monte carlo analysis of self avoiding walks in three dimensions the authors present estimates for critical exponents of self avoiding walks on a cubic lattice they treat a grand canonical ensemble of walks with free ends in a monte carlo approach and make use of real space renormalisation ideas their estimate for v is 0 59 or 0 01 the estimate for gamma does not share the same degree of accuracy however they are able to pinpoint the source of this discrepancy in addition they define a quantity chi l beta the probability that a walk starting at the origin will end outside or at the border of a cube of side l this quantity turns out to be quite suitable for a real space renormalisation group analysis

principal minors part ii the principal minor assignment problem the inverse problem of finding a matrix with prescribed principal minors is considered a condition that implies a constructive algorithm for solving this problem will always succeed is presented the algorithm is based on reconstructing matrices from their principal submatrices and schur complements in a recursive manner consequences regarding the overdeterminancy of this inverse problem are examined leading to a faster polynomial time version of the algorithmic construction care is given in the matlab implementation of the algorithms regarding numerical stability and accuracy

verification for existence of solutions of linear complementarity problems abstract recently g alefeld x chen and f potra numer math 83 1999 265 315 presented a verification method for solutions of linear complementarity problems lcps this paper is an attempt to obtain more useful information from the output of this verification method in particular existing results can only claim the nonexistence of solutions in a given interval we will use the farkas lemma to check if the interval contains a negative certification which shows the nonexistence of solutions in the whole space r n moreover we will study how to choose a good nonsingular matrix a in the interval operator for p 0 matrix linear complementarity problems we report numerical results to illustrate the efficiency of the proposed technique

worst case bounds on the point wise discretization error in boundary element method for the elasticity problem in this work point wise discretization error is bounded via interval approach for the elasticity problem using interval boundary element formulation the formulation allows for computation of the worst case bounds on the boundary values for the elasticity problem from these bounds the worst case bounds on the true solution at any point in the domain of the system can be computed examples are presented to demonstrate the effectiveness of the treatment of local discretization error in elasticity problem via interval methods

good hidden p matrix sandwiches abstract we introduce two new classes of matrices that contain the class of p matrices and can be recognized in polynomial time these classes are related to the known classes of hidden minkowski and hidden positive row diagonally dominant matrices which are subclasses of the p matrix class we show that for 3 3 matrices the class of hidden prdd matrices coincides with the class of p matrices alternative theorems for these hidden matrix classes are given and it is shown how one can use them to efficiently check membership in the classes

nonconvergence of the plain newton min algorithm for linear complementarity problems with a p matrix the plain newton min algorithm to solve the linear complementarity problem lcp for short 0 leq x perp mx q geq0 can be viewed as a semismooth newton algorithm without globalization technique to solve the system of piecewise linear equations min x mx q 0 which is equivalent to the lcp when m is an m matrix of order n the algorithm is known to converge in at most n iterations we show in this paper that this result no longer holds when m is a p matrix of order 3 since then the algorithm may cycle p matrices are interesting since they are those ensuring the existence and uniqueness of the solution to the lcp for an arbitrary q incidentally convergence occurs for a p matrix of order 1 or 2

comments regarding on stability of interval matrices with reply we note that several of the results on schur stability of interval matrices in the above paper by sezer siljak ibid vol 39 can be viewed as special cases of results obtained in a more general framework and some of the latter were previously reported in the literature in reply sezer siljak response to the issues raised in the comment

integral evaluation using the mellin transform and generalized hypergeometric functions tutorial and applications to antenna problems this is a tutorial presentation of the mellin transform mt method for the exact calculation of one dimensional definite integrals and an illustration of the application of this method to antenna electromagnetics problems once the basics have been mastered one quickly realizes that the mt method is extremely powerful often yielding closed form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals yet as opposed to other methods the mt method is very straightforward to apply it usually requires laborious calculations but little ingenuity in fact the mt method is used by mathematica to symbolically calculate definite integrals the first part of this paper is a step by step tutorial proceeding from first principles it includes basic information on mellin barnes integrals and generalized hypergeometric functions and summarizes the key ideas of the mt method in the remaining parts the mt method is applied to three examples from the antenna area the results here are believed to be new at least in the antenna electromagnetics literature in our first example we obtain a closed form expression as a generalized hypergeometric function for the power radiated by a constant current circular loop antenna this quantity has been extensively discussed recently our second example concerns the admittance of a 2 d slot antenna in both these examples the exact closed form expressions are applied to improve upon existing formulas in standard antenna textbooks in our third example finally we obtain a very simple expression for an integral arising in recent unpublished studies of unbounded biaxially anisotropic media

expansion and estimation of the range of nonlinear functions many verification algorithms use an expansion f x f x s x x f r n r n for x x where the set of matrices s is usually computed as a gradient or by means of slopes in the following an expansion scheme is described which frequently yields sharper inclusions for s this allows also to compute sharper inclusions for the range of f over a domain roughly speaking f has to be given by means of a computer program the process of expanding f can then be fully automatized the function f need not be differentiable for locally convex or concave functions special improvements are described moreover in contrast to other methods x x may be empty without implying large overestimations for s this may be advantageous in practical applications

perron frobenius theory for complex matrices abstract the purpose of this paper is to present a unified perron frobenius theory for nonnegative for real not necessarily nonnegative and for general complex matrices the sign real spectral radius was introduced for general real matrices this quantity was shown to share certain properties with the perron root of nonnegative matrices in this paper we introduce the sign complex spectral radius again this quantity extends many properties of the perron root of nonnegative matrices to general complex matrices various characterizations will be given and many open problems remain

a statistical study of temporally smoothed wavelet coherence the use of the wavelet coherence of two series in hypothesis testing relies on some sort of smoothing being carried out in order that the coherence estimator is not simply unity a previous study considered averaging via the use of multiple morse wavelets here we consider time domain smoothing and use of a single morlet wavelet since the morlet wavelet is complex valued we derive analytic results for the case of wavelet coherence calculated from complex valued jointly stationary and gaussian time series the temporally smoothed wavelet coherence can be written in terms of welch s overlapping segment averaging wosa spectrum estimators and by using multitaper equivalent representations for the wosa estimators we show that goodman s distribution is appropriate asymptotically and readily derive the appropriate degrees of freedom the theoretical results are verified via simulations and illustrated using solar physics data

welch method revisited nonparametric power spectrum estimation via circular overlap the objective of this paper is twofold the first part provides further insight in the statistical properties of the welch power spectrum estimator a major drawback of the welch method reported in the literature is that the variance is not a monotonic decreasing function of the fraction of overlap selecting the optimal fraction of overlap which minimizes the variance is in general difficult since it depends on the window used we show that the explanation for the nonmonotonic behavior of the variance as reported in the literature does not hold in the second part this extra insight allows one to eliminate the nonmonotonic behavior of the variance for the welch power spectrum estimator pse by introducing a small modification to the welch method the main contributions of this paper are providing extra insight in the statistical properties of the welch pse modifying the welch pse to circular overlap the variance is a monotonically decreasing function of the fraction of overlap making the method more user friendly and an extra reduction of variance with respect to the welch pse without introducing systematic errors this reduction in variance is significant for a small number of data records only

algorithmic detection and construction of n matrices abstract n matrices are real n n matrices all of whose principal minors are negative we provide i an o 2 n test to detect whether or not a given matrix is an n matrix and ii a characterization of n matrices leading to the recursive construction of every n matrix

the sum of squared logarithms inequality in arbitrary dimensions abstract we prove the sum of squared logarithms inequality ssli which states that for nonnegative vectors x y r n whose elementary symmetric polynomials satisfy e k x e k y for 1 k n and e n x e n y the inequality i log x i 2 i log y i 2 holds our proof of this inequality follows by a suitable extension to the complex plane in particular we show that the function f m c n r with f z i log z i 2 has nonnegative partial derivatives with respect to the elementary symmetric polynomials of z this property leads to our proof we conclude by providing applications and wider connections of the ssli

on p property and the column w property p matrices play an important role in the well posedness of a linear complementarity problem lcp similarly the well posedness of a horizontal linear complementarity problem hlcp is closely related to the column w property of a matrix k tuple in this paper we first consider the problem of generating p matrices from a given pair of matrices given a matrix pair d f where d is a square matrix of order m and matrix f has m rows what are the conditions under which there exists a matrix g such that d fg is a p matrix we obtain necessary and sufficient conditions for the special case when the column rank of f is m 1 a decision algorithm of complexity o m2 to check whether the given pair of matrices d f is p matrisable is obtained we also obtain a necessary and an independent sufficient condition for the general case when rank f is less than m 1 we then generalise the p matrix generating problem to the generation of matrix k tuples satisfying the column w property from a given matrix k 1 tuple that is given a matrix k 1 tuple d1 dk f where djs are square matrices of order m and f is a matrix having m rows we determine the conditions under which the matrix k tuple d1 fg1 dk fgk satisfies the column w property as in the case of p matrices we obtain necessary and sufficient conditions for the case when rank f m 1 using these conditions a decision algorithm of complexity o km2 to check whether the given matrix k 1 tuple is column w matrisable is obtained then for the case when rank f is less than m 1 we obtain a necessary and an independent sufficient condition for a special sub class of p matrices we give a polynomial time decision algorithm for p matrisability finally we obtain a geometric characterisation of column w property by generalising the well known separation theorem for p matrices

rigorous chaos verification in discrete dynamical systems abstract in this paper we show how interval analysis can be used to calculate rigorously valid enclosures of transversal homoclinic points in discrete dynamical systems the existence of such points guarantees that a smale horseshoe is embedded in the mapping which therefore is chaotic we take special interest in the 2 dimensional case and describe a method to obtain a computer assisted proof of chaos for these systems numerical results are presented for the standard map