conservation laws for conformally invariant variational problems we succeed in writing 2 dimensional conformally invariant non linear elliptic pde harmonic map equation prescribed mean curvature equations etc in divergence form these divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for weakly harmonic maps into homogeneous spaces from this form we can recover without the use of moving frame all the classical regularity results known for 2 dimensional conformally invariant non linear elliptic pde see hel it enables us also to establish new results in particular we solve a conjecture by e heinz asserting that the solutions to the prescribed bounded mean curvature equation in arbitrary manifolds are continuous and we solve a conjecture by s hildebrandt hil1 claiming that critical points of continuously differentiable elliptic conformally invariant lagrangian in two dimensions are continuous

brief paper a numerical sufficiency test for the asymptotic stability of linear time varying systems a numerical sufficiency test for the asymptotic stability of linear time varying hurwitz systems is proposed the algorithmic procedure constructs a bounding tube in which the state is guaranteed to stay the continuous time system is evaluated at discrete time instants for which successive quadratic lyapunov functions are generated the tube is constructed based on i a conservative estimate of the state evolution from a discrete time instant to the next obtained from the corresponding lyapunov function and ii re evaluation of the tube diameter at each discrete time instant to account for variations in the plant matrix the numerical test is illustrated in simulation via both a stable and an unstable system

new stability conditions for a class of linear time varying systems this paper considers the problem of asymptotic stability for linear time varying systems of the form x t a t x t some new stability conditions are proposed first two stability conditions for nonlinear time varying systems are given by using non monotonic lyapunov functions then the results obtained are extended to the linear case two stability conditions with infinite integral are derived furthermore by using the top floor function a linear matrix inequalities lmi condition and an eigenvalue criterion for asymptotic stability of systems are presented comparing with the existing results the conditions obtained allow both a t and a t are unbounded at t some numerical examples are provided to show the effectiveness of the theoretical results

new sufficient conditions for the stability of slowly varying linear systems the frozen time approach is used to state some new sufficient conditions for the stability of linear time varying systems an upper bound on the norm of the time derivative of system matrix which under different assumptions on frozen time system eigenvalues guarantees asymptotic stability or exponential stability of the system is established

fast gain scheduling on tracking problems using derivative information current gain scheduling practice is necessarily limited to slow variation in scheduling variables this paper proposes a control law which reflects the exogenous signal and its time derivative with assumption of its availability the proposed controller achieves better performance than the existents for tracking fast scheduling variables while rejecting exogenous signal

stochastic mean square performance analysis of an adaptive hammerstein filter this paper presents an almost sure mean square performance analysis of an adaptive hammerstein filter for the case when the measurement noise in the desired response signal is a martingale difference sequence the system model consists of a series connection of a memoryless nonlinearity followed by a recursive linear filter a bound for the long term time average of the squared a posteriori estimation error of the adaptive filter is derived using a basic set of assumptions on the operating environment this bound consists of two terms one of which is proportional to a parameter that depends on the step size sequences of the algorithm and the other that is inversely proportional to the maximum value of the increment process associated with the coefficients of the underlying system one consequence of this result is that the long term time average of the squared a posteriori estimation error can be made arbitrarily close to its minimum possible value when the underlying system is time invariant

exclusion theorems and the perturbation analysis of the generalized eigenvalue problem a bauer fike type theorem is proved for the eigenvalue problem ax lambda bx a generalization is then applied to obtain perturbation bounds for clusters of eigenvalues the conditioning of an eigenvalue finite or infinite is proved to be dependent on a jordan type condition number its eigenvector deficiency and the regularity of the matrix pencil a lambda b an example illustrating the perturbation bounds is given

perturbation of eigenvalues for periodic matrix pairs via the bauer fike theorems abstract in earlier papers the bauer fike technique was applied to the ordinary eigenvalue problem a x x the generalized eigenvalue problem a x b x and the matrix polynomial eigenvalue problem k 0 m k a k x 0 general multiple eigenvalues were dealt with and condition numbers were obtained for individual as well as clusters of eigenvalues in this paper we shall generalize the technique to the eigenvalue problem for regular periodic matrix pairs perturbation to eigenvalues simple or multiple finite or infinite will be considered for perturbations of any size for small perturbations clusters of eigenvalues will be considered

the jacobian determinant revisited this paper is devoted to the study of the jacobian determinant of a map g from a smooth bounded open subset of rn into rn n 2 more generally could be a smooth bounded open subset of an n dimensional manifold starting with the seminal work of c b morrey 27 y reshetnyak 32 and j ball 1 it has been known that one can define the distributional jacobian determinant det g under fairly weak assumption on g in particular it is defined for all maps g w 1 n2 n 1 and also for all

on a new adaptive lattice algorithm for recursive filters a new and simplified adaptive algorithm is presented for lattice structured recursive filters implementing the two multiplier form based on itakura and saito a comparison is also presented between the results obtained from this new algorithm and the algorithm introduced recently by parikh ahmed and stearns

an alternate stability analysis framework for adaptive control n abstract a proof is given for the uniform asymptotic stability of a class of pointwise in time stable systems of time varying ordinary differential equations the sufficient conditions for stability are shown to be naturally testable in a general adaptive control context a weak form of robust identification is found to imply robust stability of the overall closed loop adaptive control system

a new normalized relatively stable lattice structure this paper proposes a new lattice filter structure that has the following properties when the filter is linear time invariant lti it is equivalent to the celebrated gray markel lattice when the lattice parameters vary with time it sustains arbitrary rates of time variations without sacrificing a prescribed degree of stability provided that the lattice coefficients are magnitude bounded in a region where all lti lattices have the same degree of stability we also show that the resulting ltv lattice obeys an energy contraction condition this structure thus generalizes the normalized gray markel lattice which has similar properties but only with respect to stability as opposed to relative stability

fast rls type algorithm for unbiased equation error adaptive iir filtering based on approximate inverse power iteration in this paper a fast approximate inverse power aip iteration is applied to compute recursively the total least squares tls solution for unbiased equation error adaptive infinite impulse response iir filtering which is established by approximating the well known inverse power iteration with galerkin method the aip algorithm is based on an interesting modification of the inverse power iteration in which the first entry of the parameter vector is constrained to the negative one the distinctive feature of the proposed algorithm lies in its high computational efficiency which is characterized by efficient computation of the fast gain vector fgv adaptation of the interesting modification of the inverse power iteration and rank one update of the augmented correlation matrix the shift structure of the input data vector is exploited to develop a fast algorithm for computing the gain vector this fgv algorithm can be implemented at a numerical cost lower than the well known fast kalman algorithm since the first entry of the parameter vector has been fixed as the negative one and the weight vector is updated along the input data vector a very efficient aip algorithm is obtained by using the fgv algorithm the proposed aip algorithm is of computational complexity o l per iteration moreover with no need to use the well known matrix inversion lemma the aip algorithm has another attractive feature of numerical stability the proposed algorithm is shown to have global convergence simulation examples are included to demonstrate the effectiveness of the proposed aip algorithm

examination of the spr condition in output error parameter estimation abstract when the spr condition is not satisfied then there exist input signals for which the considered output error algorithm is locally unstable a condition is given which delimits the sharp stability instability boundary in the case of slow estimation whereas local stability properties are guaranteed by a more conservative signal dependent average spr condition these conditions are also illustrated by an example

adaptive iir filtering using parallel form realizations several parallel form adaptive iir infinite impulse response filters are presented including a frequency domain implementation based on the discrete fourier transform and a recursive frequency sampling structure the performance of the frequency domain adaptive iir filter is investigated in a system identification application which includes an analysis of its modeling capabilities and a discussion of the mean square error performance surface computer simulation results are presented to illustrate the robust convergence properties of the adaptive algorithm and to demonstrate the stability of the filter

simplified gradient calculation in adaptive iir lattice filters a simplified algorithm is presented for computing the gradient in adaptive iir infinite impulse response lattice filters for a filter with n zeros and n poles this algorithm requires only order n computations several computer simulations were performed to compare the performance of the proposed o n formulation and the conventional o n sup 2 formulation and no difference in their behavior was found in these simulations the full hessian and the diagonal hessian adaptive algorithms were used in a system identification configuration it is concluded that the proposed method allows the development of robust adaptive iir algorithms with a cost proportional to the filter order

multiple solutions of h systems and rellich s conjecture soit x y r 2 x 2 y 2 1 on considere une fonction u r 3 satisfaisant le systeme h u 2hu x u y sur avec l une des conditions suivantes soit dirichlet u sur soit plateau u x 2 u y 2 u x u y 0 sur u et u non decroissante sur

on the relationship between controllability indexes eigenvector assignment and deadbeat control the subspaces to which closed loop generalized eigenvectors are restricted are described in terms of the controllability indexes of the pair a b and the polynomials of minimal degree that span ker a lambda i b this characterization of the eigenspaces is then used to calculate the deadbeat controller of minimum frobenius norm

assessing asymptotic stability of linear continuous time varying systems by computing the envelope of all trajectories in this note necessary and sufficient numerical conditions for asymptotic stability and for uniform asymptotic stability of linear continuous time varying systems are derived for a given set of initial conditions a tube containing all the trajectories of the system is constructed in the state space at each instant of time there exists an initial condition inside the set such that the resulting trajectory attains the border of the tube based on the above formulation necessary and sufficient conditions for asymptotic stability and for uniform asymptotic stability are expressed through the solution of a linear differential lyapunov equation the conditions can deal with the stability of periodic systems as well one of the main characteristics of the proposed necessary and sufficient conditions is that the only assumption on the dynamical matrix of the time varying system is continuity examples from the literature illustrate the superiority of the proposed conditions when compared to other methods

relaxed conditions for the exponential stability of a class of linear time varying systems this technical note states new sufficient conditions for the exponential stability of linear time varying ltv systems of the form aeligmacr ldr a t aelig t the approach proposed derives and uses the notion of perturbed frozen time pft form that can be associated to any ltv system exploiting the bellman gronwall lemma relaxed stability conditions are then stated in terms of ldquoaveragerdquo parameter variations salient features of the approach are pointwise stability of a ldr is not required amacr ldr may not be bounded the stability conditions also apply to uncertain systems the approach is illustrated by numerical examples

a fast recursive total least squares algorithm for adaptive fir filtering this paper proposes a new fast recursive total least squares n rtls algorithm to recursively compute the tls solution for adaptive finite impulse response fir filtering the n rtls algorithm is based on the minimization of the constrained rayleigh quotient c rq in which the last entry of the parameter vector is constrained to the negative one as analysis results on the convergence of the proposed algorithm we study the properties of the stationary points of the c rq the high computational efficiency of the new algorithm depends on the efficient computation of the fast gain vector fgv and the adaptation of the c rq since the last entry of the parameter vector in the c rq has been fixed as the negative one a minimum point of the c rq is searched only along the input data vector and a more efficient n rtls algorithm is obtained by using the fgv as compared with davila s rtls algorithms the n rtls algorithm saves the 6m number of multiplies divides and square roots mads the global convergence of the new algorithm is studied by lasalle s invariance principle the performances of the relevant algorithms are compared via simulations and the long term numerical stability of the n rtls algorithm is verified

locally robust identification of linear systems containing unknown gain elements with application to adapted iir lattice models abstract we consider the identification of stable linear systems whose unknown parameters may be interpreted as feedback gains by using the output error between the true system and a model of it containing adjustable parameters we develop a recursive algorithm for estimating the unknown parameters we describe a persistency of excitation condition on the system input which guarantees a robust local convergence property for the algorithm we then apply our results to the identification of the parameters of a tapped lattice model of a linear infinite impulse response iir plant considering the identification of a lattice rather than a direct form model of a linear system is attractive due to i the simplicity of its crucial stability check and maintenance procedure for the adapted iir parametrization and ii the numerical insensitivity properties of the lattice structure reproducible simulation evidence is presented that supports our results

adaptive lattice iir filtering revisited convergence issues and new algorithms with improved stability properties several algorithms for adaptive iir filters parameterized in lattice form can be found in the literature the salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy on the other hand while computing the gradient signals that drive the direct form update algorithms is straightforward it is not so for the lattice algorithms this has led to simplified lattice algorithms using gradient approximations although in general these simplified schemes present the same stationary points as the original algorithms whether this is also true for convergent points has remained an open problem this also applies to nongradient based lattice algorithms such as hyperstability based and the steiglitz mcbride algorithms here we answer this question in the negative by showing that for several adaptive lattice algorithms there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent in addition new lattice algorithms with properties are derived they are based on the cascade lattice structure which allows the derivation of sufficient conditions for local stability

tracking characteristics of the constrained iir adaptive notch filter the tracking behavior of a constrained iir notch filter the coefficients of which are estimated using a constant step size gauss newton algorithm is studied using weak convergence theory and the concept of prescaling it is shown that the mean behavior of the adaptive filter coefficients can be studied by using an ordinary differential equation ode approximate and simple closed form results are derived for the tracking behavior of a second order notch filter computer simulations are presented to substantiate the analysis

design of robust d stable iir filters using genetic algorithms with embedded stability criterion this paper proposes a novel evolution strategy for a genetic algorithm ga this new algorithm is then applied to design robust d alpha r stable infinite impulse response iir filters unlike existing research on designing iir filters by using ga in which the stability of iir filters is tested by trial and error after the evolution of each generation of a ga the stability criterion in this paper is embedded within the evolution of each generation consequently the stability of this system can be guaranteed without the need for any other checks of the stability criterion in the evolution of each generation numerical experimental results are discussed to illustrate the soundness of the proposed evolution strategy the robustness of the iir filters is achieved by ensuring that all poles of the filters are located inside a disk d alpha r contained in the unit circle in which alpha is the center r is the radius of the disk and ialphai r 1 so in this paper a d alpha r stability criterion will be first derived and then embedded in the ga for the design of robust iir filters finally two examples will be presented to show that the designed filters remain d alpha r stable during the evolution of the ga and will provide satisfactory results

on regularity theory for n p harmonic maps into manifolds abstract in this paper we continue the investigation started in the paper da lio and schikorra 2014 of the regularity of the so called weak n p harmonic maps in the critical case these are critical points of the following nonlocal energy l s u r n s 2 u x p d x where u h s p r n n and n r n is a closed k dimensional smooth manifold and s n p we prove holder continuity for such critical points for p 2 for p 2 we obtain the same under an additional lorentz space assumption the regularity theory is in the two cases based on regularity results for nonlocal schrodinger systems with an antisymmetric potential

rigorous perturbation bounds for eigenvalues and eigenvectors of a matrix tight perturbation bounds are given for the shifts in the eigenvalues and eigenvectors of a matrix the case of simple as well as multiple eigenvalues is treated with the results tested numerically

unified stability criteria for slowly time varying and switched linear systems this paper presents a unified approach to formulating stability conditions for slowly time varying linear systems and switched linear systems the concept of total variation is generalized to the case of matrix valued functions using this generalized concept a result extending existing stability conditions for slowly time varying linear systems is derived as special cases of this result two sets of stability conditions are derived for switched linear systems which match known results in the literature a numerical example is included to further illustrate the application of the main result

application of benveniste s convergence results in the study of adaptive iir filtering algorithms it is shown that the weak convergence results of a benveniste et al ieee trans automat contr vol ac 25 p 1042 58 dec 1980 can be used to prove convergence of some adaptive infinite impulse response iir filtering algorithms the association of the algorithms with some ordinary differential equations for constant gains which parallels the theory of l ljung et al 1983 is suitable for constant gain adaptive filtering applications convergence proofs for a prefiltering algorithm for a simple constant gain version of the recursive maximum likelihood algorithm and for the well known simple hyperstable adaptive recursive filter sharf algorithm are given as examples

relative optimization for blind deconvolution we propose a relative optimization framework for quasi maximum likelihood qml blind deconvolution and the relative newton method as its particular instance special hessian structure allows fast newton system construction and solution resulting in a fast convergent algorithm with iteration complexity comparable to that of gradient methods we also propose the use of rational infinite impulse response iir restoration kernels which constitute a richer family of filters than the traditionally used finite impulse response fir kernels we discuss different choices of nonlinear functions that are suitable for deconvolution of super and sub gaussian sources and formulate the conditions under which the qml estimation is stable simulation results demonstrate the efficiency of the proposed methods

a stable adaptive hammerstein filter employing partial orthogonalization of the input signals this paper presents an algorithm that adapts the parameters of a hammerstein system model hammerstein systems are nonlinear systems that contain a static nonlinearity cascaded with a linear system in this paper the static nonlinearity is modeled using a polynomial system and the linear filter that follows the nonlinearity is an infinite impulse response iir system the adaptation of the nonlinear components is improved by orthogonalizing the inputs to the coefficients of the polynomial system the step sizes associated with the recursive components are constrained in such a way as to guarantee bounded input bounded output bibo stability of the overall system this paper also presents experimental results that show that the algorithm performs well in a variety of operating environments exhibiting stability and global convergence of the algorithm

sufficient stability bounds for slowly varying direct form recursive linear filters and their applications in adaptive iir filters this article derives a sufficient time varying bound on the maximum variation of the coefficients of an exponentially stable time varying direct form homogeneous linear recursive filter the stability bound is less conservative than all previously derived bounds for time varying iir systems the bound is then applied to control the step size of output error adaptive iir filters to achieve bounded input bounded output bibo stability of the adaptive filter experimental results that demonstrate the good stability characteristics of the resulting algorithms are included this article also contains comparisons with other competing output error adaptive iir filters the results indicate that the stabilized method possesses better convergence behavior than other competing techniques

sharp commutator estimates via harmonic extensions abstract we give an alternative proof of several sharp commutator estimates involving riesz transforms riesz potentials and fractional laplacians our methods only involve harmonic extensions to the upper half space integration by parts and trace space characterizations the commutators we investigate are jacobians more generally coifman rochberg weiss commutators chanillo s commutator with the riesz potential coifman mcintosh meyer kato ponce vega type commutators the fractional leibniz rule and the da lio riviere three term commutators we also give a new limiting l 1 estimate for a double commutator of coifman rochberg weiss type and several intermediate estimates the beauty of our method is that all those commutator estimates which are originally proven by various specific methods or by general para product arguments can be obtained purely from integration by parts and trace theorems another interesting feature is that in all these cases the cancellation effect responsible for the commutator estimate simply follows from the product rule for classical derivatives and can be traced in a precise way

cascade lattice iir adaptive filters the feedback lattice filter forms including the two multiplier form and the normalized form are examined with respect to their relationships to the feedback direct form filter specifically the transformation matrix between the lattice forms and the direct form is derived parameter and state relationships between the lattice forms and the direct form are therefore obtained an iir filter structure the cascade lattice iir structure is constructed based on this structure three iir adaptive filtering algorithms in the two multiplier form can then be developed following the gradient approach the steiglitz mcbride approach and the hyperstability approach convergence of these algorithms is theoretically analyzed using either the ode approach or the hyperstability theorem these algorithms are then simplified into forms computationally as efficient as their corresponding direct form algorithms relationships of the simplified algorithms to the direct form algorithms are also studied which disclose a consistency in algorithm structure regardless of the filter form three normalized lattice algorithms can also be derived from the two multiplier lattice algorithms experimental results show much improved performance of the normalized lattice algorithms over the two multiplier lattice algorithms and the direct form algorithms

perturbation bounds for polynomials using two different elementary approaches we derive a global and a local perturbation theorem on polynomial zeros that significantly improve the results of ostrowski acta math 72 99 257 1940 elsner et al linear algebra appl 142 195 209 1990 a comparison of different perturbation bounds shows that our results are better in many cases than the similar local result of beauzamy can math bull 42 1 3 12 1999 using the matrix theoretical approach we also improve the backward stability result of edelman and murakami proceedings of the fifth siam conference on applied linear algebra siam philapdelphia 1994 math comput 64 210 763 1995

persistence of excitation in linear systems abstract this paper develops output reachability characterizations of linear finite dimensional multivariate systems so as to translate excitation properties of system inputs to excitation properties of system outputs states or associated regression vectors such properties are of fundamental concern for convergence of algorithms involving on line identification adaptive state estimation prediction and control persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

generalization of the bauer fike theorem the bauer fike theorem for diagonalizable matrices is generalized to cases where i non diagonalizable matrices or ii only part of the spectrum is considered

fractional div curl quantities and applications to nonlocal geometric equations abstract we investigate a fractional notion of gradient and divergence operator we generalize the div curl estimate by coifman lions meyer semmes to fractional div curl quantities obtaining in particular a nonlocal version of wente s lemma we demonstrate how these quantities appear naturally in nonlocal geometric equations which can be used to obtain a theory for fractional harmonic maps analogous to the local theory firstly regarding fractional harmonic maps into spheres we obtain a conservation law analogous to shatah s conservation law and give a new regularity proof analogous to helein s for harmonic maps into spheres secondly we prove regularity for solutions to critical systems with nonlocal antisymmetric potentials on the right hand side since the half harmonic map equation into general target manifolds has this form as a corollary we obtain a new proof of the regularity of half harmonic maps into general target manifolds following closely riviere s celebrated argument in the local case lastly the fractional div curl quantities provide also a new simpler proof for holder continuity of w s n s harmonic maps into spheres and we extend this to an argument for w s n s harmonic maps into homogeneous targets this is an analogue of strzelecki s and toro wang s proof for n harmonic maps into spheres and homogeneous target manifolds respectively

traces of weighted sobolev spaces old and new abstract we give short simple proofs of uspenski s results characterizing besov spaces as trace spaces of weighted sobolev spaces we generalize uspenski s results and prove the optimality of these generalizations we next show how classical results on the functional calculus in the besov spaces can be obtained as straightforward consequences of the theory of weighted sobolev spaces

a structural view of asymptotic convergence speed of adaptive iir filtering algorithms i infinite precision implementation for pt i see ibid vol 41 no 4 p 1493 1517 1993 finite precision fp implementation is the ultimately inevitable reality of all adaptive filters including adaptive infinite impulse response iir filters this paper continues to examine the asymptotic convergence speed of adaptive iir filters of various structures and algorithms including the simple constant gain type and the newton type but under fp implementation a stochastic differential equation sde approach is used in the analysis such an approach not only greatly simplifies the fp analysis which is traditionally very involved algebraically but it also provides valuable information about the first order as well as the second order moments that the latter are not available using the ordinary differential equation ode approach the asymptotic convergence speed as well as the convergent values of the pertinent moments of fp errors are examined in terms of unknown system pole zero locations the adverse effects of lightly damped low frequency ldlf poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared the new results agree with the existing ones when reduced to the finite impulse response fir case in particular the explosive behavior of pertinent error variances of newton type iir algorithms when the forgetting factor spl lambda 1 is also concluded computer simulation verifies the predicted theoretical results

blind adaptation of stable discrete time iir filters in state space form blind deconvolution consists of extracting a source sequence and impulse response of a linear system from their convolution in the presence of system zeros close to the unit circle which give rise to very long impulse responses infinite impulse response iir adaptive structures are of use whose adaptation should be carefully designed in order to guarantee stability in this paper we propose a blind type discrete time iir adaptive filter structure realized in state space form that with a suitable parameterization of its coefficients remains stable the theory is first developed for a two pole filter whose numerical behavior is investigated via numerical experiments the proposed structure adaptation theory is then extended to a multipole structure realized as a cascade of two pole filters computer based experiments are proposed and discussed which aim at illustrating the behavior of the filter cascade on several cases of study the numerical results obtained show the proposed filters remain stable during adaptation and provide satisfactory deconvolution results

on multiple eigenvalues of matrices depending on several parameters the eigenvalues and eigenvectors as well as their derivatives of matrices depending on one or several parameters have been studied by sun j comput math 3 1985 pp 351 364 using the implicit function theorems and others but not for the more general multiple eigenvalues in this paper the mean of the multiple eigenvalues in terms of the trace operator tr the corresponding invariant subspaces and their derivatives are studied using a generalization of sun s approach the numerical aspects concerning the computation of such derivatives by direct and iterative methods e g simultaneous and inverse simultaneous iterations will be discussed briefly the main results in this paper apply to clusters of nonmultiple eigenvalues as well the implications e g on simultaneous iteration will be explored

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

sufficient conditions for stability of linear time varying systems abstract in this paper we consider sufficient conditions for the exponential stability of linear time varying systems of the form dot x t a t x t t 0 stability guaranteeing upper bounds for different measures of parameter variations are derived

stability of difference volterra equations direct liapunov method and numerical procedure abstract a procedure to construct liapunov functionals for discrete volterra equations is proposed using this procedure stability conditions are derived for general volterra difference equations some applications of the proposed procedure for obtaining stability conditions for linear multistep methods for volterra integro differential equations are presented

a structural view of stability in adaptive iir filters this correspondence deals with the stability issue in adaptive iir filters from a structural view a new condition under which the bounded input bounded output bibo stability of the filters can be ensured is derived based on this result a normal state space realization for second order iir filters is proposed it is shown that the adaptive iir filter realized with such a structure is bibo stable no matter it is implemented with infinite or finite precision this property is very important for real time applications though both the proposed and the normalized lattice based structures are bibo stable the former is simpler and has minimal pole sensitivities two adaptive iir filter structures are developed based on a cascade form of second order filters the first structure is fit for the filters whose poles are all complex and the second one is for the constrained notch filters simulations are given to demonstrate the performance of the proposed structures

control of slowly varying linear systems state feedback control of slowly varying linear continuous time and discrete time systems with bounded coefficient matrices is studied in terms of the frozen time approach this study centers on pointwise stabilizable systems these are systems for which there exists a state feedback gain matrix placing the frozen time closed loop eigenvalues to the left of a line re s gamma

the poles and zeros of a linear time varying system abstract for linear time varying discrete time and continuous time systems a notion of poles and zeros is developed in terms of factorizations of operator polynomials with time varying coefficients in the discrete time case it is shown that the poles can be computed by solving a nonlinear recursion with time varying coefficients in the continuous time case the poles can be calculated by solving a nonlinear differential equation with time varying coefficients the theory is applied to the study of the zero input response and asymptotic stability it is shown that if a time varying analogue of the vandermonde matrix is invertible the zero input response can be decomposed into a sum of modes associated with the poles stability is then studied in terms of the components of the modal decomposition

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

the fractional calderon problem low regularity and stability abstract the calderon problem for the fractional schrodinger equation was introduced in the work ghosh et al to appear which gave a global uniqueness result also in the partial data case this article improves this result in two ways first we prove a quantitative uniqueness result showing that this inverse problem enjoys logarithmic stability under suitable a priori bounds second we show that the results are valid for potentials in scale invariant l p or negative order sobolev spaces a key point is a quantitative approximation property for solutions of fractional equations obtained by combining a careful propagation of smallness analysis for the caffarelli silvestre extension and a duality argument

acoustic echo cancellation do iir models offer better modeling capabilities than their fir counterparts the adequateness of iir models for acoustic echo cancellation is a long standing question and the answers found in the literature are conflicting we use the results from rational hankel norm and least squares approximation and we recall a test that provides a priori performance levels for fir and iir models we apply this test to the measured acoustic impulse responses upon comparing the performance levels of fir and iir models with the same number of free parameters we do not observe any significant gain from the use of iir models we attribute this phenomenon to the shape of the energy spectra of the acoustic impulse responses so tested which possess many strong and sharp peaks faithful modeling of these peaks requires many parameters irrespective of the type of the model

fast fixed point neural blind deconvolution algorithm the aim of this letter is to introduce a new blind deconvolution algorithm based on fixed point optimization of a bussgang type cost function the cost function relies on approximate bayesian estimation achieved by an adaptive neuron the main feature of the presented algorithm is fast convergence that guarantees good deconvolution performances with limited computational demand as compared with algorithms of the same class

an asymptotic error analysis of identifiers and adaptive observers in the presence of parasitics the behavior of identifiers and adaptive observers in the presence of parasitics is analyzed bounds for the state parameter error are established the adaptive schemes considered are shown to be robust provided the input signal is rich for the dominant modes but does not contain high frequencies in the parasitic range the bounds indicate possibilities for reducing the error by a proper choice of the input signal

on the local stability properties of adaptive parameter estimators with composite errors and split algorithms the stability characteristics of a generalized error system structure are examined for adaptive parameter estimation systems this error system form encompasses the structure of a number of particular applications of adaptive parameter estimation theory which fall outside the framework of more familiar error system models the consequences for error system stability which derive from the added generality are analyzed it is demonstrated that when using averaging theory techniques to analyze the error system stability conditions must be augmented for the basic error system in order to ensure stability for the generalized error system the inadequacy of regressor spectral restrictions and persistent spanning conditions to guarantee local error system stability of the generalized structure is rigorously established alternative conditions which will yield such local stability are demonstrated to illustrate the concepts involved the recursive identification of parameters is examined in a parallel form realization of a linear system

perturbation bounds for the joint spectrum of commuting matrices using the clifford algebra techniques of pryde bhatia and bhattacharyya generalized the classical eigenvalue perturbation bound of henrici to the joint spectrum of commuting tuples of matrices elsner improved on this result using the techniques of pryde and chu we show that for small perturbations a smaller bound may be given than that obtained by elsner a similar result is then obtained using the technique of elsner himself

efficient lattice realizations of adaptive iir algorithms computationally efficient adaptive iir filter algorithms are presented based on lattice realizations allowing the adaptive filter stability to be easily monitored new simplified recursive in order equations relating the parameters of the direct form realization with the ones of two lattice realizations are presented these equations lead to a simplified technique to compute the regressor vector and to a general method to implement any adaptive iir algorithm using lattice realization results indicate that the proposed lattice based algorithms converge to a set of parameters that realize the same transfer function as the corresponding direct form algorithms

regularity of n 2 harmonic maps into spheres we prove holder continuity for n 2 harmonic maps from arbitrary subsets of rn into a sphere this extends a recent one dimensional result by f da lio and t riviere to arbitrary dimensions the proof relies on compensation effects which we quantify adapting an approach for wente s inequality by l tartar instead of besov space arguments which were used in the one dimensional case moreover fractional analogues of hodge decomposition and higher order poincare inequalities as well as several localization effects for nonlocal operators similar to the fractional laplacian are developed and applied this work was the author s phd thesis written in march 2010

discrete perturbation estimates for eigenpairs of fredholm operator valued functions we present perturbation estimates for eigenvalue and eigenvector approximations for a class of fredholm operator valued functions our approach is based on perturbation estimates for the generalized resolvents and the exponential convergence of the contour integration by the trapezoidal rule we use discrete residual functions to estimate the resolvents a posteriori numerical experiments are also presented

lifting degree and distributional jacobian revisited let g i 0 1 s1 if g vmo we may write g ei for some vmo this is unique modulo 2 see 13 and the earlier work 14 there is no control of bmo in terms of g bmo since we always have g bmo 2 and bmo can be arbitrarily large recall however that when g bmo is sufficiently small there is a linear estimate bmo c g bmo see 13 theorem 4 14 and remark 0 2 below we are going to establish that a norm slightly stronger than g bmo does control bmo consider for 1 p 0 s 1 the fractional sobolev space ws p i equipped with its standard seminorm

on energy critical half wave maps into mathbb s 2 s 2 we consider the energy critical half wave maps equation begin aligned partial t mathbf u mathbf u wedge nabla mathbf u 0 end aligned for mathbf u 0 t times mathbb r rightarrow mathbb s 2 we give a complete classification of all traveling solitary waves with finite energy the proof is based on a geometric characterization of these solutions as minimal surfaces with not necessarily free boundary on mathbb s 2 in particular we discover an explicit lorentz boost symmetry which is implemented by the conformal mobius group on the target mathbb s 2 applied to half harmonic maps from mathbb r to mathbb s 2 complementing our classification result we carry out a detailed analysis of the linearized operator l around half harmonic maps mathbf q with arbitrary degree m geqslant 1 and consisting of m identical blaschke factors here we explicitly determine the nullspace including the zero energy resonances in particular we prove the nondegeneracy of mathbf q moreover we give a full description of the spectrum of l by finding all its l 2 eigenvalues and proving their simplicity furthermore we prove a coercivity estimate for l and we rule out embedded eigenvalues inside the essential spectrum our spectral analysis is based on a reformulation in terms of certain jacobi operators tridiagonal infinite matrices obtained from a conformal transformation of the spectral problem posed on mathbb r to the unit circle mathbb s finally we construct a unitary map which can be seen as a gauge transform tailored for a future stability and blowup analysis close to half harmonic maps our spectral results also have potential applications to the half harmonic map heat flow which is the parabolic counterpart of the half wave maps equation

nonlinear commutators for the fractional p laplacian and applications we prove a nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions for the fractional p laplacian this implies that solutions to certain degenerate nonlocal equations are higher differentiable also weakly fractional p harmonic functions which a priori are less regular than variational solutions are in fact classical as an application we show that sequences of uniformly bounded frac n s harmonic maps converge strongly outside at most finitely many points

a sharp version of bauer fike s theorem in this paper we present a sharp version of bauer fike s theorem we replace the matrix norm with its spectral radius or sign complex spectral radius for diagonalizable matrices 1 norm and norm for non diagonalizable matrices we also give the applications to the pole placement problem and the singular system

lower bounds on the solution of lyapunov matrix and algebraic riccati equations in this note various lower bounds for all the eigenvalues of the solution matrix k of the lyapunov matrix equation are established a special case of this result is a generalization of that presented in 1 3 where lower bounds for the maximum and minimum eigenvalues of k are given moreover the approach used here enables one to establish various lower bounds for some of the largest eigenvalues of the solution matrix of the algebraic riccati equation

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

sub criticality of non local schrodinger systems with antisymmetric potentials and applications to half harmonic maps abstract we consider non local linear schrodinger type critical systems of the type 1 1 4 v v in r where is antisymmetric potential in l 2 r so m v is an r m valued map and v denotes the matrix multiplication we show that every solution v l 2 r r m of 1 is in fact in l loc p r r m for every 2 p in other words we prove that the system 1 which is a priori only critical in l 2 happens to have a subcritical behavior for antisymmetric potentials as an application we obtain the c loc 0 regularity of weak 1 2 harmonic maps into c 2 compact sub manifolds without boundary

lattice form adaptive infinite impulse response filtering algorithm for active noise control in some situations of active noise control infinite impulse response iir filters are more suitable than finite impulse response fir filters owing to the poles in the transfer function a number of algorithms have been derived for applying iir filters in active noise control however most of them use the direct form iir filter structure which faces the difficulties of checking stability and relatively slow convergence speed for noise composed of narrow band components with large power disparity to overcome these difficulties along with using the direct form iir filters a new adaptive algorithm is proposed in this paper which uses and updates the lattice form adaptive iir filter in an active noise control system full mathematical derivations of the proposed algorithm are presented and the comparison between the proposed algorithm and the commonly used filtered u lms and filtered v lms algorithms shows the superiority of the proposed algorithm

stable and efficient lattice algorithms for adaptive iir filtering previous attempts at applying lattice structures to adaptive infinite impulse response iir filtering have met with gradient computations of o n sup 2 complexity to overcome this computational burden two new lattice based algorithms are proposed for adaptive iir filtering and system identification with both algorithms of o n complexity the first algorithm is a reinterpretation of the steiglitz mcbride method 1965 while the second is a variation on the output error method state space models are employed to make the derivations transparent and the methods can be extended to other parameterizations if desired the set of possible stationary points of the algorithms is shown to be consistent with the convergent points obtained from the direct form versions of the steiglitz mcbride and output error methods whose properties are well studied the derived algorithms are as computationally efficient as existing direct form based algorithms while overcoming the stability problems associated with time varying direct form filters

necessary and sufficient conditions for parameter convergence in adaptive control a complete description of parameter convergence in model reference adaptive control may be given in terms of the spectrum of the exogenous reference input signal abstract using generalized harmonic analysis a complete description of parameter convergence in model reference adaptive control mrac is given in terms of the spectrum of the exogenous reference input signal roughly speaking if the reference signal contains enough frequencies then the parameter vector converges to its correct value if not it converges to an easily characterizable subspace in parameter space

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

boundary equations and regularity theory for geometric variational systems with neumann data we study boundary regularity of maps from two dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which at the boundary intersect perpendicularly with a support manifold for example harmonic maps or h surfaces with a partially free boundary condition in the interior it is known by the celebrated work of riviere that these maps satisfy a system with an antisymmetric potential from which one can derive the interior regularity of the solution avoiding a reflection argument we show that these maps satisfy along the boundary a system of equations which also exhibits a nonlocal antisymmetric potential that combines information from the interior potential and the geometric neumann boundary condition we then proceed to show boundary regularity for solutions to such systems