lqp dominant output feedbacks an output feedback matrix f will be said to dominate another bar f if the cost for f is not higher for any initial condition than the cost for bar f and if the cost is lower for some perhaps all initial conditions the output feedback obtained by for example the levine athans approach does not necessarily dominate the open loop feedback bar f 0 which could be unfortunate algorithms are given for finding feedbacks which dominate any given stabilizing feedback

estimating the errors on measured entropy and mutual information abstract information entropy and the related quantity mutual information are used extensively as measures of complexity and to identify nonlinearity in dynamical systems expressions for the probability distribution of entropies and mutual informations calculated from finite amounts of data exist in the literature but the expressions have seldom been used in the field of nonlinear dynamics in this paper formulae for estimating the errors on observed information entropies and mutual informations are derived using the standard error analysis familiar to physicists their validity is demonstrated by numerical experiment for illustration the formulae are then used to evaluate the errors on the time lagged mutual information of the logistic map

interaural correlation discrimination from diffuse field reference correlations just noticeable differences in interaural correlation jnds from diffuse sound field reference correlations are obtained in a three interval three alternative forced choice procedure jnds are measured for positive and negative deviations from nine narrowband reference conditions stimuli are 1 equivalent rectangular bandwidth wide noise bursts with center frequencies between 165 and 1500 hz the frequency dependent reference correlation ref is determined by the simulated interaural correlation under ideal diffuse sound field conditions results show that the interaural correlation at threshold for deviation toward the positive correlation range follows the reference curve in a nonlinear fashion for deviation toward the negative correlation range the interaural correlation at threshold is further afar the reference curve and does not markedly resemble its trend the results indicate that the previously found asymmetry for correlation discrimination from uncorrelated broadband stimuli to the pos

robust auditory localization using probabilistic inference and coherence based weighting of interaural cues robust sound source localization is performed by the human auditory system even in challenging acoustic conditions and in previously unencountered complex scenarios here a computational binaural localization model is proposed that possesses mechanisms for handling of corrupted or unreliable localization cues and generalization across different acoustic situations central to the model is the use of interaural coherence measured as interaural vector strength ivs to dynamically weight the importance of observed interaural phase ipd and level ild differences in frequency bands up to 1 4 khz this is accomplished through formulation of a probabilistic model in which the ild and ipd distributions pertaining to a specific source location are dependent on observed interaural coherence bayesian computation of the direction of arrival probability map naturally leads to coherence weighted integration of location cues across frequency and time results confirm the model s validity through statistical analyses of interaural parameter values simulated localization experiments show that even data points with low reliability i e low ivs can be exploited to enhance localization performance a temporal integration length of at least 200 ms is required to gain a benefit this is in accordance with previous psychoacoustic findings on temporal integration of spatial cues in the human auditory system

on the numerical solution of two point boundary value problems abstract this paper presents a new numerical method for the solution of linear two point boundary value problems of ordinary differential equations after reducing the differential equation to a second kind integral equation the latter are discretized via a high order nystrom scheme a somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using o n dot p2 operations where n is the number of nodes on the interval and p is the desired order of convergence thus the advantages of the integral equation formulation small condition number insensitivity to boundary layers insensitivity to end point singularities etc are retained while achieving a computational efficiency previously available only to finite difference or finite element methods keywords two point boundary value problems integral equations chebyshev polynomials approximation theory

monotone enclosure for a class of discrete boundary value problems without monotone nonlinearities abstract a new concept of a pair of upper and lower solutions is introduced for a class of discrete boundary value problems without monotone nonlinearities some comparison results are established an existence and enclosing theorem for the solutions is given in terms of upper and lower solutions a new monotone iterative scheme is proposed the numerical example is given

a trust region spectral bundle method for nonconvex eigenvalue optimization we present a nonsmooth optimization technique for nonconvex maximum eigenvalue functions and for nonsmooth functions which are infinite maxima of eigenvalue functions we prove global convergence of our method in the sense that for an arbitrary starting point every accumulation point of the sequence of iterates is critical the method is tested on several problems in feedback control synthesis

extremal problems on the set of nonnegative definite matrices abstract an optimization problem of minimizing a real valued function of certain elements of a symmetric matrix subject to this matrix being nonnegative definite is considered optimality conditions are proposed the duality result of olkin and pukelsheim 1982 is extended to a wide class of such problems applications are discussed

smooth optimization with approximate gradient we show that the optimal complexity of nesterov s smooth first order optimization algorithm is preserved when the gradient is computed only up to a small uniformly bounded error in applications of this method to semidefinite programs this means in some instances computing only a few leading eigenvalues of the current iterate instead of a full matrix exponential which significantly reduces the method s computational cost this also allows sparse problems to be solved efficiently using sparse maximum eigenvalue packages

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

localization of sound in rooms v binaural coherence and human sensitivity to interaural time differences in noise binaural recordings of noise in rooms were used to determine the relationship between binaural coherence and the effectiveness of the interaural time difference itd as a cue for human sound localization experiments showed a strong monotonic relationship between the coherence and a listener s ability to discriminate values of itd the relationship was found to be independent of other widely varying acoustical properties of the rooms however the relationship varied dramatically with noise band center frequency the ability to discriminate small itd changes was greatest for a mid frequency band to achieve sensitivity comparable to mid band the binaural coherence had to be much larger at high frequency where waveform itd cues are imperceptible and also at low frequency where the binaural coherence in a room is necessarily large rivalry experiments with opposing interaural level differences ilds found that the trading ratio between itd and ild increasingly favored the ild as coherence decreased suggesting that the perceptual weight of the itd is decreased by increased reflections in rooms

on the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues we derive some basic results on the geometry of semidefinite programming sdp and eigenvalue optimization i e the minimization of the sum of the k largest eigenvalues of a smooth matrix valued function we provide upper bounds on the rank of extreme matrices in sdps and the first theoretically solid explanation of a phenomenon of intrinsic interest in eigenvalue optimization in the spectrum of an optimal matrix the kth and k 1 st largest eigenvalues tend to be equal and frequently have multiplicity greater than two this clustering is intuitively plausible and has been observed as early as 1975 when the matrix valued function is affine we prove that clustering must occur at extreme points of the set of optimal solutions if the number of variables is sufficiently large we also give a lower bound on the multiplicity of the critical eigenvalue these results generalize to the case of a general matrix valued function under appropriate conditions

a quadratically convergent local algorithm on minimizing the largest eigenvalue of a symmetric matrix abstract optimization involving eigenvalues arise in many engineering problems we propose a new algorithm on minimizing the largest eigenvalue over an affine family of symmetric matrices under certain assumptions it is shown that if started close enough to the minimizer x the proposed algorithm converges to x quadratically the proposed algorithm can be readily extended to minimizing the largest eigenvalue over an affine family of hermitian matrices also it has been extended to minimizing sums of the largest eigenvalues of a symmetric or hermitian matrix

a measure of worst case h performance and of largest acceptable uncertainty abstract the structured singular value ssv or is known to be an effective tool for assessing robust performance of linear time invariant models subject to structured uncertainty yet all single analysis provides is a bound on the uncertainty under which stability as well as h performance level of are guaranteed where is preselectable in this paper we introduce a related quantity which provides answers for the following questions i given determine the smallest with the property that for any uncertainty bounded by an h performance level of is guaranteed ii conversely given determined the largest with the property that again for any uncertainty bounded by an h performance level of is guaranteed properties of this quantity are established and approaches to its computation are investigated both unstructured uncertainty and structured uncertainty are considered

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

interaural correlation discrimination ii relation to binaural unmasking many theoretical models of binaural interaction assume that sensitivity to interaural correlation underlies binaural unmasking this paper explores the extent to which sensitivity to changes in interaural correlation implied by results from binaural detection experiments are consistent with sensitivity to changes in interaural correlation measured directly in correlation discrimination experiments the vehicle for this exploration is a simplified model of the underlying processes assumed by many models of binaural unmasking for the detection of narrow band signals in the presence of broadband noise consideration is given to psychometric function slopes detection thresholds bandwidth effects duration effects level effects and interaural parameter effects although many of the results obtained from our analysis are consistent with the notion that the cue in binaural detection tasks is a change in interaural correlation some significant inconsistencies are noted

some recent developments of numerov s method abstract this paper is a survey of some recent developments of numerov s method for solving nonlinear two point boundary value problems the survey consists of three different parts the existence uniqueness of a solution computational algorithm for computing a solution and some extensions of numerov s method the sufficient conditions for the existence and uniqueness of a solution are presented some of them are best possible various iterative methods are reviewed including picard s iterative method modified newton s iterative method monotone iterative method and accelerated monotone iterative method in particular two more direct monotone iterative methods are presented to save computational work each of these iterative methods not only gives a computational algorithm for computing a solution but also leads to an existence and uniqueness theorem the estimate on the rate of convergence of the iterative sequence is given the extensions of numerov s method to a coupled problem and a general problem are addressed the numerical results are presented to validate the theoretical analysis

the normalized interaural correlation accounting for nospi thresholds obtained with gaussian and low noise masking noise recently j acoust soc am 103 2578 2589 1998 and j acoust soc am 103 2573 2577 1998 independently reported that greater masking of interaurally phase reversed s tones was produced by diotic low noise noise than by diotic gaussian noise based on quantitative analyses eddins and barber suggested that their results could not be accounted for by assuming that listeners judgments were based on constant criterion changes in the normalized interaural correlation produced by adding the s signal to the diotic masker in particular they showed that a model like the one previously employed by j acoust soc am 100 3774 3784 1996 predicted an ordering of thresholds between the conditions of interest that was opposite to that observed bernstein and trahiotis computed the normalized interaural correlation subsequent to half wave square law rectification and low pass filtering the parameters of which were chosen to mimic peripheral auditory processing in this report it is demonstrat

on analyticity of functions involving eigenvalues abstract let a z be an n n complex matrix whose elements depend analytically on z c m it is well known that any individual eigenvalue of a z may be nondifferentiable when it coalesces with others in this paper we investigate the analycity property of functions on the eigenvalues z 1 z n z of a z we first introduce the notion of functions that are symmetric with respect to partitions it is then shown that if a function c n c is analytic at a where a c m and is symmetric with respect to a certain partition induced by a then the composite function g z 1 z n z is analytic at a when z is real a z is symmetric or hermitian and the aforementioned assumptions hold so that g z is analytic at a we also derive formulae for its first and second order partial derivatives we apply the results to several problems involving eigenvalues

monotone methods for a boundary value problem of second order discrete equation abstract the comparison and existence results of the upper and lower solutions are established for a boundary value problem of second order discrete equation a monotone iterative scheme is proposed the local as well as global existence and uniqueness of the solution are obtained the global convergence of the iteration is investigated the convergence rate of the iteration is analyzed and compared some examples are given

interaural correlation sensitivity sensitivity to differences in interaural correlation was measured for 1 3 erb wide bands of noise using a 2ifc task at six frequencies 250 500 750 1000 1250 and 1500 hz the sensitivity index d was measured for discriminations between a number of fixed pairs of correlation values cumulative d functions were derived for each frequency and condition the d for discriminating any two values of correlation may be recovered from the cumulative d function by the difference between cumulative d s for these values two conditions were employed the noisebands were either presented in isolation narrow band condition or in the context of broad contiguous flanking bands of correlated noise fringed condition the cumulative d functions showed greater sensitivity to differences in correlation close to 1 than close to 0 at low frequencies but this difference was less pronounced in the fringed condition also a more linear relationship was observed when cumulative d was plotted as a function of the equivalent signal to noise ratio snr in db for each correlation value rather than directly against correlation the equivalent snr was the snr at which the interaural correlation in an nos stimulus would equal the interaural correlation of the noise used in the experiment the maximum cumulative d declined above 750 hz this decline was steeper for the fringed than for the narrow band condition for the narrow band condition the total cumulative d was variable across listeners all cumulative d functions were closely fitted using a simple two parameter function the complete data sets averaged across listeners from the fringed and narrow band conditions were fitted using functions to describe the changes in these parameters over frequency in order to produce an interpolated family of curves that describe sensitivity at frequencies between those tested these curves predict the spectra recovered by the binaural system when complex sounds such as speech are masked by noise

spectro temporal factors in two dimensional human sound localization this paper describes the effect of spectro temporal factors on human sound localization performance in two dimensions 2d subjects responded with saccadic eye movements to acoustic stimuli presented in the frontal hemisphere both the horizontal azimuth and vertical elevation stimulus location were varied randomly three types of stimuli were used having different spectro temporal patterns but identically shaped broadband averaged power spectra noise bursts frequency modulated tones and trains of short noise bursts in all subjects the elevation components of the saccadic responses varied systematically with the different temporal parameters whereas the azimuth response components remained equally accurate for all stimulus conditions the data show that the auditory system does not calculate a final elevation estimate from a long term order 100 ms integration of sensory input instead the results suggest that the auditory system may apply a multiple look strategy in which the final estim

accelerated monotone iterative methods for a boundary value problem of second order discrete equations abstract an accelerated monotone iterative method for a boundary value problem of second order discrete equations is presented this method leads to an existence comparison theorem as well as a computational algorithm for the solutions the monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function some numerical results are presented to illustrate the monotone convergence of the iterative sequences and the rate of convergence of the iterations

interaural correlation discrimination i bandwidth and level dependence measurements of interaural cross correlation jnds from two reference correlations at several bandwidths were obtained for constant total power and constant spectral power gaussian noise at a reference correlation of 1 the results indicate that for bandwidths less than or equal to 115 hz the jnd remains at a constant value of approximately 0 004 and monotonically increases discrimination performance degrades to approximately 0 04 as bandwidth increases above 115 hz at a reference correlation of 0 the jnd decreases discrimination performance improves from approximately 0 7 to 0 35 as the bandwidth increases from 3 to 115 hz and remains at a constant value of approximately 0 35 for bandwidths greater than 115 hz a decrease in the spectral level causes an increase in the jnds at a reference correlation of 1 and no change in the jnds at a reference correlation of 0 of the three models tested none is able to completely describe all of the empirical results

existence of dominant solutions in linear output feedback the standard lq regulator is known to be a dominant controller in the sense that the optimal cost is minimal for all initial states x 0 in r n in general static or dynamic output feedback controllers do not have this dominance property in this note it is shown that in the general multivariable case and for the original cost functional a dynamic output feedback controller using an observer is dominant if and only if the observer is perfectly initialized

finite element approximation to the extremal eigenvalue problem for inhomogenous materials in this paper an extremal eigenvalue problem corresponding to an inhomogeneous membrane which is composed of two different materials with different densities is investigated the convergence of the finite element discretization and the error order for the smallest eigenvalue are obtained a monotonic decreasing algorithm is presented to solve the discretized problem and numerical examples are given to demonstrate the error estimation as well as the efficiency of the method

on discrete boundary value problems arising in transport phenomena for the discrete boundary value problems arising in transport processes we provide comparison results these results are used to develop monotone iterative methods for the construction of the maximal and minimal solutions in a sector the advantage of this technique is that the successive approximations are the solutions of the initial and terminal value problems numerical illustration showing the sharpness as well the importance of the obtained results is also included

nondifferentiable optimization algorithm for designing control systems having singular value inequalities it has been known for some time that many control system design requirements can be expressed as differentiable inequalities more recently it has been shown that important structural properties such as robustness and low noise sensitivity can be expressed as nondifferentiable inequalities involving the singular values of a system or return difference transfer function matrix this paper presents an optimization algorithm which permits all these constraints to be considered

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

measurements of the binaural temporal window using a detection task two experiments investigated the shape of the binaural temporal window using a detection task in experiment 1 a 10 ms tone burst was presented binaurally out of phase during a burst of white noise which changed from being interaurally uncorrelated to correlated and back to uncorrelated the tone occurred during the correlated portion of the noise in one interval of each 2i fc trial detection thresholds were recorded using a 2 down 1 up adaptive procedure thresholds were measured for different durations of correlated noise 0 960 ms frequencies of tone burst 125 250 500 and 1000 hz and levels of noise 20 30 40 and 50 db spl hz window shapes based on nine candidate functions were fitted to the data using the assumption that the binaural masking release was related to the overall interaural correlation of noise admitted by the window fitted windows included both a forward and a backward lobe gaussian functions tended to give closer fits than exponential and rounded exponential functions and simple functions gave more parsimonious fits that those which included dynamic range limiting terms using simple gaussian fits the shape of the window was largely independent of frequency and level and the windows for individual listeners had equivalent rectangular durations ranging from 55 to 188 ms the asymmetry was variable although forward lobes were generally shorter than backward lobes experiment 2 ruled out the possibility that the forward lobe might be an artefact caused by distraction of the listener when the interaural phase change in the noise closely followed the signal in this experiment the out of phase tone was presented during a burst of partially correlated noise which changed after a variable interval to a fully correlated noise thresholds for detecting the tone rose i e performance worsened as the interval was increased distraction would have produced the opposite effect

large scale optimization of eigenvalues optimization problems involving eigenvalues arise in many applications let x be a vector of real parameters and let a x be a continuously differentiable symmetric matrix function of x we consi

monotone iterative methods for a general class of discrete boundary value problems abstract in this paper we shall offer comparison results as well as monotone iterative schemes for the construction of solutions to a very general class of discrete boundary value problems the discrete system we consider includes in particular the n th order prototype systems finite as well as infinite discrete delay equations and discrete integral equations further the boundary conditions we consider include the initial terminal periodic and transport type problems numerical examples illustrating the usefulness of the proposed schemes to a variety of boundary value problems are also included

an interior point method for minimizing the maximum eigenvalue of a linear combination of matrices we consider the problem of finding lambda opt mathop inf limits x in r m lambda max a 0 sum limits i 1 m x i a i 1 and an optimal solution xopt if it exists here the a i are given symmetric matrices in ir n n for 0 i m and max a is the largest eigenvalue of a matrix a problem 1 can be rewritten as a convex differentiable problem with a positive definite constraint positive definiteness can easily be verified numerically via cholesky decomposition moreover the cone of positive definite matrices a is characterized by the domain of the smooth convex barrier function log det a

parallel monotone iterative relaxation methods for a class of two dimensional discrete boundary value problems abstract a parallel monotone iterative relaxation method for a class of two dimensional discrete boundary value problems is established and the sequence of iterations is shown to converge monotonically either from above or below to a solution of the problem this monotone convergence results yields a parallel computational algorithm as well as an existence comparison result for the solutions to compute the sequence of iterations the thomas algorithm can be used in the same fashion as for one dimensional problem the existence and comparison results of the upper and lower solutions are given the local as well as global existence uniqueness of the solution are obtained the global convergence of the iterations is investigated and the influence of the parameters on the rate of convergence of the iterations is analyzed numerical results are given to corroborate the analytical results

numerov s method for strongly nonlinear two point boundary value problems abstract by a proper transformation a class of strongly nonlinear two point boundary value problems are transformed into semilinear problems so that the well known numerov s method can be applied some applications and numerical results are presented to demonstrate the efficiency of the approach

on minimizing the largest eigenvalue of a symmetric matrix abstract optimization problems involving eigenvalues arise in many engineering problems in this paper we consider the problem of minimizing the largest eigenvalue over an affine family of symmetric matrices this problem has a variety of applications such as the stability analysis of dynamic systems or the computation of structured singular values given 0 we give an optimality condition which ensures that the largest eigenvalue is within error bound of the solution also a new line search rule is proposed and it is shown to have good descent properties when the multiplicity of the largest eigenvalue the solution is known a new algorithm for the optimization problem under consideration is proposed some numerical experiments on the proposed algorithm are presented

semi definite matrix constraints in optimization positive semi definite matrix constraints arise in a number of optimization problems in which some or all of the elements of a matrix are variables such as the educational testing and matrix modification problems the structure of such constraints is developed including expressions for the normal cone feasible directions and their application to optimality conditions a computational framework is given within which these concepts can be exploited and which permits the quantification of second order effects the matrix of lagrange multipliers in this formulation is shown to have an important relationship to the characterization of the normal cone modifications of various iterative schemes in nonlinear programming are considered in order to develop an effective algorithm for the educational testing problem and comparative numerical experiments are described it is shown that a particular choice of the penalty parameter for an l 1 exact penalty function is appropriate for this type of problem the be

on problems involving eigenvalues for uncertain matrices by structured singular values this technical note considers problems that involve eigenvalues of uncertain matrices expressed in linear fractional form using the structured singular value mu and the skewed structured singular value nu in particular positive definiteness conditions maximum and minimum eigenvalues and generalized eigenvalues of uncertain matrices are expressed using mu and nu the obtained results allow us to acquire information of an uncertain matrix efficiently by the existing computational tools that provide practically useful approximations to the values of mu and nu

some new results on optimal and suboptimal regulators of the lq problem with output feedback the lq linear quadratic regulator problem with output feedback is considered in the problem studies an output feedback control is determined such that the cost is j the optimal cost for the lq problem with state feedback or beta j with some constant beta 1 a set of sufficient conditions is given for determining such optimal and suboptimal output feedback control laws