interference rejection in ffh systems using least squares estimation techniques a fast frequency hopped ffh receiver which uses a prewhitening filter to reject narrowband interference is described by using an appropriate fractional tap spacing it is shown that interference can be estimated independently of the desired signal bit error rate results are presented for the receiver for linear square law combining the results compare favorably to those obtained by a near optimal automatic gain control agc combining technique the performance of the prewhitening filter interference rejection method is shown to be superior to that of a nonparametric self normalizing receiver finally simulation results for an ffh receiver using the complex least mean square lms algorithm to update the prewhitening filter coefficients are presented

a controllability test for general first order representations we derive a new controllability rank test for general first order representations the criterion generalizes the well known controllability rank test for linear input state systems as well as a controllability rank test by mertzios et al for descriptor systems

adaptive lattice filters for cdma overlay this paper presents the behavior of reflection coefficients of a stochastic gradient lattice sgl filter applied to a code division multiple access overlay system analytic expressions for coefficients for a two stage filter are derived in a rayleigh fading channel with the presence of narrow band interference and additive white gaussian noise it is shown that the coefficients of the lattice filter exhibit separate tracking and convergent properties and that compared to an lms filter the lattice filter provides fast rate of convergence while having good capability of narrow hand interference suppression

defect correction and domain decomposition for second order boundary value problems abstract highly accurate approximation is obtained through the techniques of defect correction and domain decomposition for second order elliptic boundary value problems on a disc the basic solution is computed using the schwarz domain decomposition procedure and bilinear galerkin finite element approximation on each subdomain to get an o h 2 accurate basic solution in higher order discrete sobolev norms the defects are then computed using high order polynomials lagrange polynomials or splines to get as many o h 2 corrections as possible

rejection of multiple narrow band interference in both bpsk and qpsk ds spread spectrum systems the performance of direct sequence spread spectrum systems using a suppression filter in the presence of multiple narrow band interference with rational spectral densities is analyzed both bpsk and qpsk systems are considered and analytical expressions for both the means square error of the filter output and the performance improvement are established when the bandwidths of the narrow band components of the interference are all small approximate expressions are obtained and used to provide further insight into the behavior of the system results are presented for the limiting case when the bandwidths approach aero i e when multiple narrow band interference becomes multiple sinusoidal interference

a comparison of some global methods for solving two point boundary value problems a numerical comparison is made between three codes which implement global methods for solving two point boundary value problems the codes compared are a collocation method colsys a deferred correction method pasva 3 and a deferred correction method based on mono implicit runge kutta formulae hagron although the difficulty of conducting a fair comparison of complex codes is widely recognised it is nevertheless of great practical importance to try to gauge the relative performance of different codes and the three codes considered in this paper are particularly appropriate for numerical comparison by choosing a test set which includes both smooth and increasingly stiff problems some interesting characteristics of the codes are noted and some recommendations regarding their use are made

numerical solution by lmms of stiff delay differential systems modelling an immune response we consider the application of linear multistep methods lmms for the numerical solution of initial value problem for stiff delay differential equations ddes with several constant delays which are used in mathematical modelling of immune response for the approximation of delayed variables the nordsieck s interpolation technique providing an interpolation procedure consistent with the underlying linear multistep formula is used an analysis of the convergence for a variable stepsize and structure of the asymptotic expansion of global error for a fixed stepsize is presented some absolute stability characteristics of the method are examined implementation details of the code difsub dde being a modification of the gear s difsub are given finally an efficiency of the code developed for solution of stiff ddes over a wide range of tolerances is illustrated on biomedical application model

a new narrowband interference suppression scheme for spread spectrum cdma communications this paper presents a new nonlinear approach for narrowband interference nbi suppression in code division multiple access cdma systems the proposed scheme is an adaptive nonlinear predictor that consists of an n 1 level quantizer four adders and two adaptive linear filters where n is the number of users in the cdma system both adaptive filters have the same coefficients at each iteration one for feedforward estimation of nbi and the other for feedback compensation for the estimated result it could be regarded as an improved version of the nonlinear predictor with offset outputs presented recently by wang et al 1996 computer simulation results support that the improved offset predictor performs much better than the original one under the same complexity as compared with the nearly optimal approximate conditional mean filter it achieves almost the same performance even at very low signal to noise ratio but involves much less complexity

the complex lms adaptive algorithm transient weight mean and covariance with applications to the ale the transient and steady state mean and covariance of the complex valued lms adaptive element weights are investigated when the inputs are samples from circularly normal processes it is shown that the data covariance diagonalizing matrix also diagonalizes the weight covariance matrix this result permits describing the complete transient behavior of the adaptive line enhancer ale weight covariance matrix in closed form for the case of multiple equal power narrow band statistically independent orthogonal rayleigh fading sinusoids in broad band noise based on these transient covariance results it is shown that for any stage of adaptation there exists an optimum ale gain constant that minimizes the excess mean squared prediction error this result is of particular significance when processing time limited data

a general realization theory for higher order linear differential equations in this note we show that the geometric quotient under a natural group action of the generalized state space systems recently considered by schumacher kuijper and geerts is algebraically isomorphic to the space of a homogeneous autoregressive system this result essentially follows from work of stromme published earlier in the algebraic geometry literature in particular these generalized state space systems represent a realization of the space of homogeneous autoregressive systems

nonlinear techniques for interference suppression in spread spectrum systems the binary nature of direct sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose the case of a gaussian interferer with known autoregressive parameters is considered using simulations it is shown that an approximate conditional mean acm filter of the masreliez type performs significantly better than the optimum linear kalman bucy filter for the case of interferers with unknown parameters the nature of the nonlinearity in the acm filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction two versions of this filter are considered one in which the filter coefficients are updated using the widrow lms algorithm and another in which the coefficients are updated using an approximate gradient algorithm simulations indicate that the nonlinear filter with lms updates performs substantially better than the linear filter for both narrowband gaussian and single tone interferers whereas the gradient algorithm gives slightly better performance for gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer

numerical treatment of o d es the theory ofa methods almost all commonly used methods for o d es and their most miscellaneous compositions area methods i e they can be reduced toz o z j az j 1 h x j 1 z j 1 z j h z j s a s s j 1 1 m this paper presents a general theory fora methods and discusses its practical consequences an analysis of local discretization error l d e accumulation results in a general order criterium and reveals which part of the l d e effectively influences the global error this facilitates the comparison of methods and generalizes considerably the concept of error constants it is shown as a consequence that the global error cannot be safely controlled by the size of the l d e and that the conventional error control may fail in important cases furthermore butcher s effective order methods the concept of nordsieck forms and gear s interpretation of lineark step schemes as relaxation methods are generalized the stability of step changing is shortly discussed

on the stability of interpolatory variable stepsize adams methods in nordsieck form this paper considers the stability of adams methods that vary the stepsize using the interpolation technique of nordsieck sufficient conditions sometimes necessary on the stepsize ratios h n 1 h n that imply the stability of adams methods with different strategies of stepsize variation are obtained this study extends previous results on this subject by gear and tu siamj numer anal 11 1974 pp 1025 1043 and skeel and jackson siam j numer anal 20 1983 pp 840 853

feedback design for regularizing descriptor systems this paper surveys numerical techniques for the regularization of descriptor generalized state space systems by proportional and derivative feedback we review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the weierstras canonical form three condensed forms display the controllability and observability properties of a descriptor system the condensed forms are obtained through orthogonal equivalence transformations and rank decisions so they may be computed by numerically stable algorithms in addition the condensed forms display whether a descriptor system is regularizable i e when the system pencil can be made to be regular by derivative and or proportional output feedback and if so what index can be achieved also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

direct controllability and observability time domain conditions of singular systems controllability and observability criteria for singular systems using direct formulas in the time domain are introduced the method used is based on a direct expansion of the transfer function matrix via a leverrier type algorithm hence no decomposition of the state space model is needed and the criteria are implementable on a digital computer the compact form of the matrices might be helpful in other analysis as well as synthesis problems in singular systems

the order of accuracy for deferred corrections using uncentered end formulas a result of christiansen and russell siam j numer math 35 1980 pp 21 33 on the order of accuracy of an iterated deferred corrections algorithm of lentini and pereyra siam j numer math 14 1977 pp 91 111 is improved at the same time providing a realistic example for a theoretical framework developed by the author for proving accuracy results for deferred corrections

a theoretical framework for proving accuracy results for deferred corrections general techniques are described for proving accuracy results for deferred correction solutions to differential equations these techniques apply also to computational estimates of the local discretization error the proofs avoid the necessity of demonstrating the existence of asymptotic expansions of the global error in powers of some meshsize parameter

on the stability of variable stepsize nordsieck bdf methods in this paper the stability of backward differentiation methods that vary the stepsize using the interpolation technique of nordsieck is considered conditions for the stability of the methods are obtained the study is an extension of previous results given by gear and tu 3 and skeet and jackson 14

the close relationships between methods for solving two point boundary value problems the well conditioning of a boundary value problem is shown to be related to bounding two quantities one involving the boundary conditions and the other involving the green s function in the case of a solution dichotomy they are related to known stability results these results easily explain why difficulties arise using superposition and reduced superposition it is shown how multiple shooting overcomes these difficulties by relating its matrix conditioning to the underlying boundary value problem some factorization methods for the multiple shooting method are considered these show the close relationships between multiple shooting the stabilized march and invariant imbedding and one factorization leads to an efficient new way to implement each of these three methods many of the results apply for collocation and finite difference methods too finally it is shown both theroetically and computationally when matrix compactification can lead to difficulty

on the probability density function of the lms adaptive filter weights the joint probability density function of the weight vector in least mean square lms adaptation is studied for gaussian data models an exact expression is derived for the characteristic function of the weight vector at time n 1 conditioned on the weight vector at time n the conditional characteristic function is expanded in a taylor series and averaged over the unknown weight density to yield a first order partial differential difference equation in the unconditioned characteristic function of the weight vector the equation is approximately solved for small values of the adaption parameter and the weights are shown to be jointly gaussian with time varying mean vector and covariance matrix given as the solution to well known difference equations for the weight vector mean and covariance matrix the theoretical results are applied to analyzing the use of the weights in detection and time delay estimation simulations that support the theoretical results are also presented

a new theoretical approach to runge kutta methods runge kutta rk methods are treated here as linear multistage methods within the author s concept of a methods as a consequence the traditional difference in treatment of rk methods and linear multistep methods vanishes in particular it is not necessary to consider elementary differentials it is shown how the order of a rk method depends on the error constants of its stages and the conditions nonlinear equations for order p are generated from a very simple recursion

stability of multistep methods on variable grids this paper is concerned with the stability of multistep methods for ordinary initial value problems on grids with variable mesh sizes a necessary and sufficient condition for stability is given from which generalizations of recent results by gear et al and by zlatev can be obtained as special cases as an application the stability of the variable bdf formulas is treated

gaussian collocation via defect correction for the numerical integration of boundary value problems for first order ordinary differential systems collocation on gaussian points is known to provide a powerful method in this paper we introduce a defect correction method for the iterative solution of such high order collocation equations the method uses the trapezoidal scheme as the basic discretization and an adapted form of the collocation equations for defect evaluation the error analysis is based on estimates of the contractive power of the defect correction iteration it is shown that the iteration produceso h 2 convergence rates for smooth starting vectors a new result is that the iteration damps all kind of errors so that it can also handle non smooth starting vectors successfully

new nonlinear algorithms for estimating and suppressing narrowband interference in ds spread spectrum systems it has been shown that the narrowband nb interference suppression capability of a direct sequence ds spread spectrum system can be enhanced considerably by processing the received signal via a prediction error filter the conventional approach to this problem makes use of a linear filter however the binary ds signal that acts as noise in the prediction process is highly non gaussian thus linear filtering is not optimal vijayan and poor 1990 first proposed using a nonlinear approximate conditional mean acm filter of the masreliez 1975 type and obtained significant results this paper proposes a number of new nonlinear algorithms our work consists of three parts 1 we develop a decision directed kalman ddk filter that has the same performance as the acm filter but a simpler structure 2 using the nonlinear function in the acm and the ddk filters we develop other nonlinear least mean square lms filters with improved performance 3 we further use the nonlinear functions to develop nonlinear recursive least squares rls filters that can be used independently as predictors or as interference identifiers so that the acm or the ddk filter can be applied simulations show that our nonlinear algorithms outperform conventional ones

the stability of one step schemes for first order two point boundary value problems the stability of a finite difference scheme is related explicitly to the stability of the continuous problem being solved at times this gives materially better estimates for the stability constant than those obtained by the standard process of appealing to the stability of the numerical scheme for the associated initial value problem

the convergence of variable stepsize variable formula multistep methods in this paper variable stepsize variable formula multistep methods for the numerical solution of ordinary differential equations are considered some more general results on stability than are given in the papers of gear tu siam j numer anal 11 1974 pp 1025 1043 and gear watanabe siam j numer anal 11 1974 pp 1044 1058 are obtained further the asymptotic behavior of the error in the variable stepsize fixed formula case is studied finally the above study is extended to predictor corrector methods

a matrix euclidean algorithm induced by state space realization an efficient algorithm is developed for determining the greatest common left divisor gcld of two polynomial matrices knowing this divisor allows for several immediate applications in coding theory a noncatastrophic convolutional encoder can be derived from an arbitrary one in systems theory irreducible matrix fraction descriptions of transfer function matrices can be found in linear algebra the greatest common divisor can be seen as a basis for a free module generated by the columns of the matrices the approach taken is based on recent ideas from systems theory a minimal state space realization is obtained with minimal calculations and from this the controllability matrix is analyzed to produce the gcld it will be shown that the derived algorithm is a natural extension of the euclidean algorithm to the matrix case

performance analysis of narrow band interference rejection techniques in ds spread spectrum systems linear least squares estimation llse techniques can provide an effective means of suppressing narrow band interference in direct sequence ds spread spectrum systems in the results presented here analytical expressions for bit error rate are derived for two ds spread spectrum systems under the conditions of either tone or narrowband gaussian interference it is shown that the most common llse filter design can lead to performance inferior to that of various other filter designs however results are also presented demonstrating that an llse filter design motivated by the structure of the maximum likelihood receiver leads to consistently superior performance the performance of a system using this new design criterion is compared with that of an approximation to the maximum likelihood ml receiver for the tone interference model and with that of the exact ml receiver for the gaussian interference finally it is shown that the bit error rate estimate obtained from application of a gaussian approximation for the test statistic is overly pessimistic for the systems studied here

defect correction from a galerkin viewpoint we consider the numerical solution of systems of nonlinear two point boundary value problems by galerkin s method an initial solution is computed with piecewise linear approximating functions and this is then improved by using higher order piecewise polynomials to compute defect corrections this technique including numerical integration is justified by typical galerkin arguments and properties of piecewise polynomials rather than the traditional asymptotic error expansions of finite difference methods

the stability of variable stepsize nordsieck methods conditions are given for the stability of multistep methods that vary the stepsize using the interpolation technique of nordsieck if the stepsize selection function is variation bounded then these methods are stable alternatively there exist constants a b c depending on the method and satisfying a leqq b 1 c such that if the stepsize ratio h n 1 h n satisfies either 0 h n 1 h n leqq a or b h n 1 h n leqq c then the method is stable as the frequency of stepsize changing decreases the methods become more stable in the sense that the intervals defined by a b and c are larger tables and graphs are given for the adams and backward differentiation methods indicating how stability changes with frequency of changing stepsize in particular it is shown that k 1 value adams formulas k leqq 6 are stable for 0 h n 1 h n leqq c that is it is shown that stability is maintained whenever the stepsize is decreased by an arb

highly continuous interpolants for one step ode solvers and their application to runge kutta methods we suggest a general method for the construction of highly continuous interpolants for one step methods applied to the numerical solution of initial value problems of odes of arbitrary order for the construction of these interpolants one uses along with the numerical data of the discrete solution of a problem provided by a typical one step method at endstep points high order derivative approximations of this solution this approach has two main advantages it allows an easy way of construction of high order runge kutta and nystrom interpolants with reduced cost in additional function evaluations that also preserve the one step nature of the underlying discrete ode solver moreover for problems which are known to possess a solution of high smoothness the approximating interpolant resembles this characteristic a property that on occasion might be desirable an analysis of the stability behavior of such interpolatory processes is carried out in the general case a new numerical technique concerning the accurate determination of the stability behavior of numerical schemes involving higher order derivatives and or approximations of the solution from previous grid points over nonequidistant meshes is presented this technique actually turns out to be of a wider interest as it allows us to infer in certain cases more accurate results concerning the stability of for example the bdf formulas over variable stepsize grids moreover it may be used as a framework for analyzing more complex and supposedly more promising types of methods as they are the general linear methods for first and second order differential equations many particular variants of the new method for first order differential equations that have good prospects of finding a practical implementation are fully analyzed with respect to their stability characteristics a detailed application concerning the construction of c 2 and c 3 continuous extensions for some fifth and sixth order runge kutta pairs supplemented by a detailed study of the local truncation error characteristics of a class of interpolants of this type is also provided various numerical examples show in these cases several advantages of the newly proposed technique with respect to function evaluation cost and global error behavior in comparison with others currently in use

permutation filter lattices a general order statistic filtering framework a general nonlinear filtering framework permutation order statistic filter lattices is introduced which defines a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system as well as the possible noise contamination permutation filters much like polynomial filters are flexible and modular where instead of having polynomial expansions we have permutation lattice expansions at the simplest level in the filter lattice permutation filters reduce to either a simple linear fir or to an order statistic os filter but at higher levels in the lattice the obtained filters can model complicated nonlinear systems more accurately while still preserving their robust properties in order to enhance the robustness of permutation fitters we develop spl alpha trimmed permutation indicators and their associated filter lattices we conclude by presenting simulation examples where permutation filters are used in nonlinear system identification and in the rejection of narrowband interference in a direct sequence multiple access system this paper thus extends the potential of order statistic filters which have been shown to be somewhat limited in general nonlinear estimation problems

elements of a general theory of composite integration methods this contribution is a survey of results on general linear methods after an introduction into the concept of a methods which is a slight generalization of general linear methods and its main results rk methods are presented in the a method notation which offers the following advantages a the order conditions are obtained from a simple recursion without relying on rooted trees or elementary differentials b they appear in a transparent form as orthogonality relations in dependence of the error constants of the stages of the rk method c their orthogonal structure permits elegant existence proofs and yields new auxiliary conditions d the error accumulation within the stages of the method is completely understood the proof of the main result on rk methods theorem 5 is simplified

interference rejection in pn spread spectrum systems with ls linear phase fir filters the effects of a narrowband interference present in a pseudonoise pn spread spectrum system can be minimized by using digital whitening techniques a new efficient block ls algorithm for the design of an fir filter with linear phase is derived and used as a whitening filter simulations are carried out to demonstrate the effectiveness of the ls optimum linear phase filter in suppressing a narrowband interference in a pn spread spectrum system comparisons to previously used methods are made the simulations showed an improvement in the output snr on the order of 4 5 db over already existing schemes

adaptive enhancement of finite bandwidth signals in white gaussian noise the steady state behavior of the adaptive line enhancer ale is analyzed for stationary inputs consisting of finite bandwidth signals embedded in a white gaussian noise wgn background analytic expressions for the weights and output of the lms adaptive filter are derived as functions of input signal bandwidth and snr as well as ale length and bulk delay the steady state gain in broad band snr from input to output is derived as a function of these same four variables for fixed ale parameters and input snr it is shown that this gain increases as the input signal becomes narrower and approaches the sinusoidal limit it is emphasized that because the correlation time of finite bandwidth signals is limited excessively large values of the ale bulk delay parameter result in diminished gain furthermore there is an optimal filter length whose value depends upon signal bandwidth and snr for which the broad band gain is maximized these results demonstrate the importance of including the effects of algorithm noise in analyzing the performance of real time adaptive processors

on behaviors and convolutional codes it is well known that a convolutional code is essentially a linear system defined over a finite field in this paper we elaborate on this connection we define a convolutional code as the dual of a complete linear behavior in the sense of willems 1979 using ideas from systems theory we describe a set of generalized first order descriptions for convolutional codes as an application of these ideas we present a new algebraic construction for convolutional codes

an approximate statistical analysis of the widrow lms algorithm with application to narrow band interference rejection the widrow lms algorithm is considered for the implementation of an adaptive prewhitening filter in a direct sequence ds spread spectrum receiver exact expressions for the steady state tapweight covariance matrix and resulting average excess mean square error are developed for the real lms algorithm when the input contains a random binary sequence used to model a pseudonoise spreading sequence it is shown here that the output samples of the adaptive filter possess approximately gaussian statistics under the conditions of slow convergence and a large number of filter taps using this approximation expressions for the resulting bit error rate ber when the adaptive algorithm is used to suppress a fading gone jammer are developed and numerical results obtained from these expressions are compared to simulation results for the ds receiver

order conditions for general linear methods we describe the derivation of order conditions without restrictions on stage order for general linear methods for ordinary differential equations this derivation is based on the extension of the albrecht approach proposed in the context of runge kutta and composite and linear cyclic methods this approach was generalized by jackiewicz and tracogna to two step runge kutta methods by jackiewicz and vermiglio to general linear methods with external stages of different orders and by garrappa to some classes of runge kutta methods for volterra integral equations with weakly singular kernels this leads to general order conditions for many special cases of general linear methods such as diagonally implicit multistage integration methods nordsieck methods and general linear methods with inherent runge kutta stability exact coefficients for several low order methods with some desirable stability properties are presented for illustration

leverrier s algorithm for singular systems an algorithm is presented which allows the computation of the transfer function of a singular system from its state space description without inverting a polynomial matrix this algorithm is an extension of the leverrier algorithm for the more general case of singular systems and it reduces the computational cost

a general class of two step runge kutta methods for ordinary differential equations a general class of two step runge kutta methods that depend on stage values at two consecutive steps is studied these methods are special cases of general linear methods introduced by butcher and are quite efficient with respect to the number of function evaluations required for a given order general order conditions are derived using the approach proposed recently by albrecht and examples of methods are given up to the order 5 these methods can be divided into four classes that are appropriate for the numerical solution of nonstiff or stiff differential equations in sequential or parallel computing environments

constrained adaptive filtering algorithms asymptotic convergence properties for dependent data the convergence properties of constrained adaptive filtering algorithms are established the constraint is in the form of a bounded set in which the filter s coefficients must lie a recursive procedure that converges to the deterministic solution of the constrained linear mean square estimation problem is obtained using an appropriate contraction mapping the recursion is used to derive the adaptive algorithm for the filter coefficients bounds on the mean square error of the coefficients bounds on the mean square error of the estimates of the filter coefficients and on the excess error of the input signal estimate are derived for processes that are either strong mixing or asymptotically uncorrelated the algorithms use a moving window of size n on the data from one adaptation step to the next however tighter bounds can be obtained when a skipped sampling mechanism is used

impulsive smooth behavior in multimode systems part ii minimality and equivalence this is the second part of a two part study of linear multimode systems in the first part it was argued that the behavior of such a system on an interval between switches should be described in a framework that allows for impulses at the switching instant and both first order and polynomial representations were introduced that satisfy this requirement here we determine the conditions under which first order representations are minimal we also show how two minimal representations of the same behavior are related this leads in particular to an appropriate state space isomorphism theorem the minimality conditions are given a dynamic interpretation

impulsive smooth behavior in multimode systems part i state space and polynomial representations abstract a switched or multimode system is one that can switch between various modes of operation we consider here switched systems in which the modes of operation are characterized as linear finite dimensional systems not necessarily all of the same mcmillan degree when a switch occurs from one of the modes to another of lower mcmillan degree the state space collapses and an impulse may result followed by a smooth evolution under the new regime this paper is concerned with the description of such impulsive smooth behavior on a typical interval we propose an algebraic framework modeled on the class of impulsive smooth distributions as defined by hautus both state space and polynomial representations are considered and we discuss transformations between the two forms

advance in the theory of variable stepsize variable formula methods for ordinary differential equations the theory of the constant stepsize constant formula methods cscfm s for solving initial value problems for ordinary differential equations ode s is well developed however the integration methods are often used as variable stepsize variable formula methods vsvfm s in the codes for automatic solution of ode s this fact explains why it is necessary to develop a rigorous theory for the vsvfm s also results obtained until now in the efforts to develop a theory for the vsvfm s are presented in a systematic way and compared with the well known results for cscfm s the comparison is used to outline the directions in which further efforts in the attempt to improve the theoretical results and to obtain new results are most needed the integration methods can be separated into two large groups implicit methods and explicit methods including here the predictor corrector schemes it is discussed what kind of results are needed for each of these two groups assume that a set f of cscfm s is given from a practical point of view it is highly desirable that the cscfm s belonging to set f have the following property if every cscfm from set f is consistent zero stable and convergent then any vsvfm induced by the cscfm s of set f is also consistent zero stable and convergent for a sufficiently large class of grids a theorem concerning a class of cscfm s with this property is presented the application of this theorem in the selection of methods for solving large systems of ode s arising after the space discretization of air pollution models is discussed it is explained why the vsvfm s based on this class provide a very efficient computational process in the treatment of air pollution models

a new recurrence for computing runge kutta truncation error coefficients researchers investigating runge kutta methods use truncation error coefficients to derive formulas and assess their quality in this paper albrecht s recurrence for generating order conditions is refined to produce truncation error coefficients the refined recurrence provides a fast and relatively simple way of calculating truncation error coefficients of the albrecht expansion for general runge kutta methods

error probabilities for ds spread spectrum systems using an ale for narrow band interference rejection the effects of the least mean squares adaptive line enhancer ale weight misadjustment errors on the bit error rate are investigated for a direct sequence spread spectrum binary communication system in the presence of strong narrowband interference the converged ale weights are modeled as the parallel connection of a deterministic fir finite impulse response filter and a random fir filter the statistics of the random filter are derived assuming the output of the random filter to be primarily due to the jammer convolved with random filter weights this output is shown to be nongaussian and to cause significant error rate degradation in comparison to a gaussian model error probability expressions are derived for the bit error rate evaluated numerically and compared to the corresponding error probabilities for a gaussian model for the random filter output for some typical system parameter values and error probabilities it is shown that the gaussian model yields performance results that are too optimistic by several decibels

thirteen ways to estimate global error various techniques that have been proposed for estimating the accumulated discretization error in the numerical solution of differential equations particularly ordinary differential equations are classified described and compared for most of the schemes either an outline of an error analysis is given which explains why the scheme works or a weakness of the scheme is illustrated

quivers geometric invariant theory and moduli of linear dynamical systems we use geometric invariant theory and the language of quivers to study compactifications of moduli spaces of linear dynamical systems a general approach to this problem is presented and applied to two well known cases we show how both lomadze s and helmke s compactification arises naturally as a geometric invariant theory quotient both moduli spaces are proven to be smooth projective manifolds furthermore a description of lomadze s compactification as a quot scheme is given whereas helmke s compactification is shown to be an algebraic grassmann bundle over a quot scheme this gives an algebro geometric description of both compactifications as an application we determine the cohomology ring of helmke s compactification and prove that the two compactifications are not isomorphic when the number of outputs is positive