a numerical method for an integro differential equation with memory in banach spaces qualitative properties a first order method is considered for the discretization in time of an integro differential equation which can be written as d alpha u t a u t f t 1 alpha 2 where a d a subset x to x is a sectorial operator in a banach space x qualitative properties of the numerical solution such as contractivity and positivity are studied a numerical illustration is provided

fully hierarchical divergence conforming basis functions on tetrahedral cells with applications a new set of hierarchical divergence conforming vector basis functions on curvilinear tetrahedrons is presented the basis can model both mixed and full order polynomial spaces to arbitrary order as defined by raviart and thomas and nedelec solenoidal and non solenoidal components are separately represented on the element except in the case of the mixed first order space for which a decomposition procedure on the global mesh wide level is presented therefore the hierarchical aspect of the basis can be made to extend down to zero polynomial order the basis can be used to model divergence conforming quantities such as electromagnetic flux and current density fluid velocity etc within numerical methods such as the finite element method fem or integral equation based methods the basis is ideally suited to p adaptive analysis the paper concludes with two example applications the first is the fem based solution of the linearized acoustic vector wave equation where it is shown how the decomposition into solenoidal components and their complements can be used to stabilize the method at low frequencies the second is the solution of the electric field volume integral equation for electromagnetic scattering analysis where the benefits of the decomposition are again demonstrated

from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

generalised autoregressive models and their trajectories the set of classical ar models is not compact so that a sequence of ar models may fail to converge to anything reasonable a compactification leads to ar models with arbitrary singularity at infinity these limit ar models are represented by pairs of polynomial and proper rational matrices satisfying certain compatibility condition it is shown that they produce trajectories in a very natural way then the classical equivalence theorem is extended to them stating that two ar models having the same behaviour are equivalent

stability of switched linear differential systems we study the stability of switched systems whose dynamic modes are described by systems of higher order linear differential equations not necessarily sharing the same state space concatenability of trajectories at the switching instants is specified by gluing conditions i e algebraic conditions on the trajectories and their derivatives at the switching instants we provide sufficient conditions for stability based on lmis for systems with general gluing conditions we also analyse the role of positive realness in providing sufficient polynomial algebraic conditions for stability of two modes switched systems with special gluing conditions

realization by inspection we investigate which first order representations can be obtained from high order representations of linear systems by inspection that is just by rearrangement of the data under quite weak conditions it is possible to obtain minimal realizations in the so called pencil form under stronger conditions one can obtain minimal realizations in standard state space form by inspection the development is based on a reformulation of the realization problem as a problem of finding a complete set of basis vectors for the nullspace of a given constant matrix since no numerical computation is needed the realization method in particular is suitable for situations in which some of the coefficients are symbolic rather than numerical

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

system structure and singular control the general continuous time linear quadratic control problem is considered it is shown that recently developed linear system theoretic properties and algorithms play an important role in solving this singular control problem

hierarchical divergence conforming nedelec elements for volumetric cells a new family of hierarchical divergence conforming vector bases is proposed for tetrahedral prism and brick cells these functions span the divergence conforming reduced curl spaces of nedelec the bases are constructed from orthogonal scalar polynomials to enhance their linear independence which is a simpler process than an orthogonalization applied to the final vector functions specific functions are tabulated to order 6 5 these basis are intended for use with numerical solutions of volume integral equations or differential equations containing divergence operators

an extension of the 1 9 problem we consider the rational approximation of a perturbed exponential function 1 f z u 0 z u 1 z e z on the negative real axis r with u 0 and u email protected 0 being rational functions building upon results from the solution of the 1 9 problem by gonchar and rakhmanov it is shown that rational best approximants to f share the fast asymptotic convergence of rational approximants to the exponential function despite the fact that the functions 1 may differ substantially from the exponential our main result is that for email protected z fixed we have 2 limn email protected f rn n k r 1 n 19 28902549 h with h being the same halphen constant as that already known from the solution of the 1 9 problem and r n m r n m f r being a rational best approximant with denominator and numerator degrees at most n and m in the uniform norm on r to the function f of type 1 further it is shown that the convergence on r which is characterized by 2 extends to compact subsets of the complex plane c and also to hankel contours in email protected r and this extension holds with the same asymptotic rate of convergence h many of the results for rational best approximants extend also to rational close to best approximants which by our definition are rational approximants with a convergence behavior on r that is comparable in an nth root sense to that of the best approximants r n n the asymptotic distribution of the poles of approximants is studied and determined in the present paper we present only results complete proofs are not given however some of the main ideas of the proofs are sketched

solving the volume integral equations of electromagnetic scattering time harmonic electromagnetic scattering by inhomogeneous three dimensional structures within a free space environment can be described by electric and magnetic field volume integral equations involving the free space green function a comprehensive set of galerkin projection formulations also known as moment methods for the numerical solution of these equations is presented together with comparative numerical results such formulations are widely used for particle scattering analysis optical near field calculation etc results are obtained with higher order divergence and curl conforming basis functions on iso parametric tetrahedral meshes the results demonstrate that all formulations converge with similar accuracy in the case of an analytically solvable test problem when modeling flux densities as solution variables it is argued that solenoidal function spaces should be used rather than the standard divergence conforming function spaces this assertion is supported by the results some of the formulations involve solving for curl conforming fields such fields can be discretized with fewer unknowns than divergence conforming ones implying lower computational costs additionally some formulations yield system matrices which are approximately halfway sparse meaning that computational costs will be down by a factor of 2 when iterative solvers are employed which is the case for the widely used fast methods

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

solvability conditions consistency and weak consistency for linear differential algebraic equations and time invariant singular systems the general case we present several solvability concepts for linear differential algebraic equations daes with constant coefficients on the positive time axis as well as for the associated singular systems and investigate under which conditions these concepts are met next we derive necessary and sufficient conditions for global consistency of initial conditions for the dae as well as for the system and generalize these conditions with respect to our concept of weak consistency our distributional approach enables us to generalize results in an earlier paper where singular systems are assumed to have a regular pencil in the sense of gantmacher in particular we establish that global weak consistency in the system sense is equivalent to impulse controllability

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

numerical evaluation of two and three parameter mittag leffler functions the mittag leffler ml function plays a fundamental role in fractional calculus but very few methods are available for its numerical evaluation in this work we present a method for the efficient computation of the ml function based on the numerical inversion of its laplace transform lt an optimal parabolic contour is selected on the basis of the distance and the strength of the singularities of the lt with the aim of minimizing the computational effort and reducing the propagation of errors numerical experiments are presented to show accuracy and efficiency of the proposed approach the application to the three parameter ml also known as prabhakar function is also presented

numerical characterization of divergence conforming constrained basis functions for surface integral equations this paper presents an algebraic method of generating arbitrary order basis functions suitable for use in moment methods the basis functions are constructed by enforcing a set of suitable constraints on a more general set of functions leading to a matrix representation of the constraint condition the desired bases are then found through use of the singular value decomposition divergence conforming constrained bases are presented for quadrilateral meshes for use in electric and magnetic field integral equations appropriate constraints for enforcing normal continuity at cell boundaries are discussed a variety of problems are analyzed using the constrained bases and results show that the constrained bases exhibit exponential convergence for smooth structures and produce systems whose condition numbers grow relatively slowly with increasing basis order

the exponentially convergent trapezoidal rule it is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line the mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity it is linked with computational methods all across scientific computing including algorithms related to inverse laplace transforms special functions complex analysis rational approximation integral equations and the computation of functions and eigenvalues of matrices and operators

hierarchical curl conforming nedelec elements for triangular prism cells new curl conforming hierarchical vector basis functions are developed for triangular prism cells these bases are constructed by taking the product of base vectors with scalar orthogonal polynomials and are shown to maintain linear independence as their polynomial order is increased the procedure for constructing these basis functions is described and specific functions are tabulated for orders up to 6 5 these bases are compatible with recently proposed hierarchical bases for tetrahedral and hexahedral cells and will maintain tangential continuity with those bases if used in a mesh containing multiple cell shapes

transformations of linear systems under external equivalence abstract we consider systems of linear differential and algebraic equations in which some of the variables are distinguished as external variables two systems are called equivalent if the set of solutions for the external variables is the same for both systems we give an operational form for this definition of equivalence i e we describe a set of system transformations having the property that two systems are equivalent if and only if they can be taken into each other by transformations from that set next an algorithm is described to transform a given system in general form to a system in minimal state space form this algorithm differs from existing methods in that it first takes the equations to first order form so that each subsequent step can be formulated and interpreted in state space terms we also compute the structure indices in terms of a state space description in nonminimal form and use this to prove the minimality of the end result of the algorithm finally an application is shown to the problem of ill posedness of feedback connections

volume surface integral equation method based on higher order hierarchical vector basis functions for em scattering and radiation from composite metallic and dielectric structures this paper presents a novel galerkin type method of moments solution of the volume surface integral equation vsie which is developed for the analysis of electromagnetic scattering and radiation from composite metallic and dielectric structures our new scheme utilizes curved tetrahedral elements and curved triangular patches for geometric modeling and the associated higher order hierarchical vector hohv basis functions for volume surface current modeling in contrast to the previous studies on higher order vsie our scheme which is reported for the first time in vsie is much more flexible in comparison with the conventional low order scheme our scheme requires much less memory and computational time for the same accuracy level numerical results are provided to demonstrate the accuracy efficiency and flexibility of our scheme

hierarchal vector boundary elements and p adaption for 3 d electromagnetic scattering this paper describes the development of new vector boundary elements for solving electromagnetic em scattering problems the new elements are suitable for the magnetic field integral equation mfie electrical field integral equation efie or the combination field integral equation cfie the basis functions are assigned to the edges of an element rather than to its nodes the new element guarantees the continuity of the normal component of the surface current across element edges furthermore the basis functions are hierarchical from linear to higher order which enables one to use the new elements in a p adaption scheme

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

a test for behavioral equivalence external equivalence of behavioral representations is investigated within an impulsive smooth framework as an attendant problem initial value consistency is also considered explicit necessary and sufficient conditions are derived applying the external equivalence result to conventional system representations reveals some interesting interpretations

divergence conforming constrained basis functions for hexahedral volume elements this communication presents an algebraic method for constructing arbitrary order divergence conforming basis functions on hexahedral volume elements the appropriate constraints within and on the boundaries of elements are provided in particular the handling of faces where quantities are discontinuous is discussed the resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased

curl conforming hierarchical vector bases for triangles and tetrahedra a new family of hierarchical vector bases is proposed for triangles and tetrahedra these functions span the curl conforming reduced gradient spaces of nedelec the bases are constructed from orthogonal scalar polynomials to enhance their linear independence which is a simpler process than an orthogonalization applied to the final vector functions specific functions are tabulated to order 6 5 preliminary results confirm that the new bases produce reasonably well conditioned matrices

adaptive fast and oblivious convolution in evolution equations with memory to approximate convolutions which occur in evolution equations with memory terms a variable step size algorithm is presented for which advancing n steps requires only o n log n operations and o log n active memory in place of o n 2 operations and o n memory for a direct implementation a basic feature of the fast algorithm is the reduction via contour integral representations to differential equations which are solved numerically with adaptive step sizes rather than the kernel itself its laplace transform is used in the algorithm the algorithm is illustrated on three examples a blowup example originating from a schrodinger equation with concentrated nonlinearity chemical reactions with inhibited diffusion and viscoelasticity with a fractional order constitutive law

a spectral order method for inverting sectorial laplace transforms laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered a spectral order parallelizable method for their numerical inversion is proposed the method takes into account the available information about the errors arising in the evaluations several numerical illustrations are provided

a fast algorithm for parabolic pde based inverse problems based on laplace transforms and flexible krylov solvers we consider the problem of estimating parameters in large scale weakly nonlinear inverse problems for which the underlying governing equations is a linear time dependent parabolic partial differential equation a major challenge in solving these inverse problems using newton type methods is the computational cost associated with solving the forward problem and with repeated construction of the jacobian which represents the sensitivity of the measurements to the unknown parameters forming the jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time dependent parabolic partial differential equations corresponding to multiple sources and receivers we propose an efficient method based on a laplace transform based exponential time integrator combined with a flexible krylov subspace approach to solve the resulting shifted systems of equations efficiently our proposed solver speeds up the computation of the forward and adjoint problems thus yielding significant speedup in total inversion time we consider an application from transient hydraulic tomography tht which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests the algorithms discussed are applied to a synthetic example taken from tht to demonstrate the resulting computational gains of this proposed method

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

smooth impulsive linear systems interconnections smooth impulsive sm imp linear systems are the smallest class containing all classical linear systems and stable with respect to limits in this article we show that they behave well under the operation of interconnection namely it turns out that the mcmillan degree of a regular interconnection is always equal to the sum of the mcmillan degrees of the components in other words all regular interconnections of sm imp linear systems automatically are regular feedback interconnections for this more general class of linear systems we also study the regular interconnection problem

a parallel method for time discretization of parabolic problems based on contour integral representation and quadrature we treat the time discretization of an initial value problem for a homogeneous abstract parabolic equation by first using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane then transforming this into a real integral on the finite interval and finally applying a standard quadrature formula to this integral the method requires the solution of a finite set of elliptic problems with complex coefficients which are independent and may therefore be done in parallel the method is combined with spatial discretization by finite elements

invariant subspaces and invertibility properties for singular systems the general case abstract open loop definitions and properties of several subspaces for general singular systems are characterized by means of a fully algebraic distributional framework simple recursive algorithms for producing these spaces as well as related duality aspects turn out to follow directly from these definitions next we provide definitions and conditions for two notions of left right invertibility of a general singular system in terms of our distributions subspaces and rosenbrock s system matrix and we show which conditions represent the gap between our invertibility concepts finally we prove that in many cases left right invertibility is equivalent to left right invertibility of the system matrix

hierarchical curl conforming nedelec elements for quadrilateral and brick cells new curl conforming hierarchical vector basis functions are developed for quadrilateral and hexahedral cells these bases are constructed from orthogonal polynomials and are shown to maintain superior linear independence as their polynomial order is increased the procedure for constructing these basis functions is described and general expressions are provided for an arbitrary order

double higher order large domain volume surface integral equation method for analysis of composite wire plate dielectric antennas and scatterers a novel double higher order large domain galerkin type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for analysis of composite dielectric and metallic radiation scattering structures combining the volume integral equation vie approach for dielectric parts and the surface integral equation sie approach for metallic parts of the structure the technique employs lagrange type interpolation generalized hexahedra and quadrilaterals of arbitrary geometrical mapping orders for the approximation of geometry and hierarchical divergence conforming polynomial vector basis functions of arbitrary expansion orders for the approximation of currents within the elements the double higher order vsie vie sie method is extensively validated and evaluated against the analytical solutions and the numerical results obtained by alternative higher order methods

smooth impulsive linear systems axiomatic description abstract paper concerns with linear systems having arbitrary singularity at infinity these systems deserve to study since they are limits of familiar classical linear systems an axiomatic description of such systems is obtained

dempster shafer evidential theory for the automated selection of parameters for talbot s method contours and application to matrix exponentiation in this paper the dempster shafer theory of evidential reasoning is applied to the problem of optimal contour parameters selection in talbot s method for the numerical inversion of the laplace transform the fundamental concept is the discrimination between rules for the parameters that define the shape of the contour based on the features of the function to invert to demonstrate the approach it is applied to the computation of the matrix exponential via numerical inversion of the corresponding resolvent matrix training for the dempster shafer approach is performed on random matrices the algorithms presented have been implemented in matlab the approximated exponentials from the algorithm are compared with those from the rational approximation for the matrix exponential returned by the matlab expm function

parabolic and hyperbolic contours for computing the bromwich integral some of the most eectiv e methods for the numerical inversion of the laplace transform are based on the approximation of the bromwich contour integral the accuracy of these methods often hinges on a good choice of contour and several such contours have been proposed in the literature here we analyze two recently proposed contours namely a parabola and a hyperbola using a representative model problem we determine estimates for the optimal parameters that dene these contours an application to a fractional diusion equation is presented

optimizing talbot s contours for the inversion of the laplace transform talbot s method for the numerical inversion of the laplace transform consists of numerically integrating the bromwich integral on a special contour by means of the trapezoidal or midpoint rules in this paper we address the issue of parameter selection in the method for the particular situation when parabolic pdes are solved in the process the well known subgeometric convergence rate o exp c sqrt n of this method is improved to the geometric rate o exp c n with n the number of nodes in the integration rule the value of the maximum decay rate c is explicitly determined numerical results for two versions of the heat equation are presented with the choice of parameters derived here the rule of thumb is that to achieve an accuracy of 10 ell at any given time the associated elliptic problem has to be solved no more than ell times

nineteen dubious ways to compute the exponential of a matrix twenty five years later in principle the exponential of a matrix could be computed in many ways methods involving approximation theory differential equations the matrix eigenvalues and the matrix characteristic polyn

computing functions of very large matrices with small tt qtt ranks by quadrature formulas abstract the computation of matrix functions using quadrature formulas and rational approximations of very large structured matrices using tensor trains tt and quantized tensor trains qtt is considered here the focus is on matrices with a small tt qtt rank some analysis of the error produced by the use of the tt qtt representation and the underlying approximation formula used is also provided promising experiments on exponential power mittag leffler and logarithm function of multilevel toeplitz matrices that are among those which generate a low tt qtt rank representation are also provided confirming that the proposed approach is feasible

volume integral equation with higher order hierarchical basis functions for analysis of dielectric electromagnetic scattering an efficient method of moments mom solution of volume electric field integral equation v efie with a kind of higher order basis functions is presented to model scattering from a dielectric object with arbitrary shapes and inhomogenuity this method is based on both higher order geometrical modeling and higher order current modeling which is realized using a family of higher order hierarchical vector hhov basis functions to expand the equivalent volume electric currents within curvilinear volume elements this higher order scheme of mom results in a significant reduction in meshing density and number of unknowns leading to a remarkable reduction of memory and cpu time in comparison with conventional low order mom while the accuracy of the solution remains at a comparable level numerical results agree with analytical solutions or with simulation results obtained by commercial software demonstrating the accuracy convergence efficiency flexibility and adaptability of the new approach

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

computing a alpha log a and related matrix functions by contour integrals new methods are proposed for the numerical evaluation of f mathbf a or f mathbf a b where f mathbf a is a function such as mathbf a 1 2 or log mathbf a with singularities in infty 0 and mathbf a is a matrix with eigenvalues on or near 0 infty the methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving jacobi elliptic functions the convergence is geometric so that the computation of f mathbf a b is typically reduced to one or two dozen linear system solves which can be carried out in parallel

realization of autoregressive equations in pencil and descriptor form a linear system described by autoregressive equations with a given input output structure cannot be transformed to standard state space form if the implied input output relation is nonproper instead a realization in descriptor form must be used in this paper it is shown how to obtain minimal descriptor realizations from autoregressive equations without separating finite and infinite frequencies and without going through a reduction process external equivalence is used so that even situations in which there is no transfer matrix can be considered the approach is based on the so called pencil representation of linear systems and it is shown that there is a natural realization of autoregressive equations in pencil form in this way the link between the realization theories of willems and fuhrmann can also be clarified

representability of impulsive input output behaviors in descriptor form abstract it is known that the descriptor representation of linear smooth behaviors imposes no constraints on the partitioning of external variables into inputs and outputs the issue is reconsidered here in the setting of impulsive behaviors in this context there are two different descriptor representations that may be used the conventional form and the unconventional one it is shown that the conventional descriptor form again does not constrain the choice of inputs and outputs but the unconventional form does the latter representation only allows input output partitionings in which inputs are dirac free this notion is newly defined here

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

nonconformal discretization of electric current volume integral equation with higher order hierarchical vector basis functions a nonconformal discretization of the electric current volume integral equation jvie is presented for the electromagnetic scattering analysis of inhomogeneous dielectric objects this jvie is based on higher order geometrical and current modeling where curved tetrahedral elements and higher order hierarchical vector hohv basis functions are adopted in order to implement the nonconformal discretization the half face based hohv basis function is introduced to address the nonconformal volumetric elements compared to the conventional low order conformal nonconformal vie our nonconformal hohv based jvie has the advantage of improving the computational efficiency and accuracy compared to the previous vie discretized by other higher order functions our nonconformal jvie is based on the higher order geometric modeling and the hohv bases in order to improve the efficiency the basis expansion and recombination technique is introduced to significantly accelerate the matrix filling moreover the flexibility of basis order selection is further enhanced by the mixed order schemes numerical results are given to demonstrate its accuracy efficiency and flexibility

computing the gamma function using contour integrals and rational approximations some of the best methods for computing the gamma function are based on numerical evaluation of hankel s contour integral for example temme evaluates this integral based on steepest descent contours by the trapezoid rule here we investigate a different approach to the integral the application of the trapezoid rule on talbot type contours using optimal parameters recently derived by weideman for computing inverse laplace transforms relatedly we also investigate quadrature formulas derived from best approximations to exp z on the negative real axis following cody meinardus and varga the two methods are closely related and both converge geometrically we find that the new methods are competitive with existing ones even though they are based on generic tools rather than on specific analysis of the gamma function

output feedback pole placement with dynamic compensators derives a new rank condition which guarantees the arbitrary pole assignability of a given system by dynamic compensators of degree at most q by using this rank condition the authors establish several new sufficiency conditions which ensure the arbitrary pole assignability of a generic system the authors proofs also come with a concrete numerical procedure to construct a particular compensator which assigns a given set of closed loop poles