delay dependent h filtering for singular markovian jump systems with general uncomplete transition probabilities this paper is devoted to the investigation of the delay dependent h filtering problem for a kind of singular markovian jump time delay systems with general unknown transition probabilities in this model the transition rates of the jumping process are assumed to be partly available that is some elements have been exactly known some ones have been merely known with lower and upper bounds others may have no information to use using the lyapunov functional theory a stochastically stable filter is designed to guarantee both the mean square exponential admissibility and a prescribed level of h performance for the singular markovian jump time delay systems with general unknown transition probabilities a sufficient condition is derived for the existence of such a desired filter in terms of linear matrix inequalities lmis a numerical example is provided to demonstrate the effectiveness of the proposed theory

imposing boundary conditions in sinc method using highest derivative approximation sinc approximate methods are often used to solve complex boundary value problems such as problems on unbounded domains or problems with endpoint singularities a recent implementation of the sinc method li c and wu x numerical solution of differential equations using sinc method based on the interpolation of the highest derivatives applied mathematical modeling 31 1 2007 1 9 in which sinc basis functions are used to approximate the highest derivative in the governing equation of the boundary value problem is evaluated for structural mechanics applications in which interlaminar stresses are desired we suggest an alternative approach for specifying the boundary conditions and we compare the numerical results for analysis of a laminated composite timoshenko beam implementing both li and wu s approach and our alternative approach for applying the boundary conditions for the timoshenko beam problem we obtain accurate results using both approaches including transverse shear stress by integration of the 3d equilibrium equations of elasticity the beam results indicate our approach is less dependent on the selection of the sinc mesh size than li and wu s sihd we also apply sihd to analyze a classical laminated composite plate for the plate example we experience difficulty in obtaining a complete system of equations using li and wu s approach for our approach we suggest that additional necessary information may be obtained by applying the derivatives of the boundary conditions on each edge using this technique we obtain accurate results for deflection and stresses including interlaminar stresses by integration of the 3d equilibrium equations of elasticity our results for both the beam and the plate problems indicate that this approach is easily implemented has a high level of accuracy and good convergence properties

new results on stability analysis of markovian switching singular systems this paper addresses the stability problem for linear continuous time markovian switching singular systems considering the inherent state jump behavior at the switching instants a necessary and sufficient condition of exponential stability in the mean square sense for the markovian switching singular system is established in terms of linear matrix inequalities by means of a stochastic lyapunov approach based on the obtained stability result sufficient conditions of exponential stability in the mean square sense for the markovian switching singular system with uncertain and partly unknown transition probability are presented numerical examples are presented to illustrate the effectiveness of the proposed approach

robust h sup spl infin filtering for uncertain markovian jump systems with mode dependent time delays this paper considers the problem of robust h sup spl infin filtering for uncertain markovian jump linear systems with time delays which are time varying and depend on the system mode the parameter uncertainties are time varying norm bounded the aim of this problem is to design a markovian jump linear filter that ensures robust exponential mean square stability of the filtering error system and a prescribed l sub 2 induced gain from the noise signals to the estimation error for all admissible uncertainties a sufficient condition for the solvability of this problem is obtained the desired filter can be constructed by solving a set of linear matrix inequalities an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

integrated local petrov galerkin sinc method for structural mechanics problems an integrated local petrov galerkin sinc method is introduced and applied to static structural mechanics problems the method approximates the highest derivative in the local weak form of the governing equation on a rectangular grid and the lower derivatives and unknown function are found by numerical indenite integration we suggest that the essential boundary conditions may be applied by the traditional penalty method or by a method in which the stiness matrix is reduced to eliminate dependent degrees of freedom we propose and compare the performance of three basis functions in terms of their accuracy and convergence properties for two problems a one dimensional tapered bar and a two dimensional plane stress elasticity problem our results indicate that the present method can provide greater accuracy than the sinc method based on interpolation of highest derivative an integration based collocation method suggested by li and wu li c and wu x numerical solution of dierential equations using sinc method based on

on camera calibration with linear programming and loop constraint linearization a technique for calibrating a network of perspective cameras based on their graph of trifocal tensors is presented after estimating a set of reliable epipolar geometries a parameterization of the graph of trifocal tensors is proposed in which each trifocal tensor is linearly encoded by a 4 vector the strength of this parameterization is that the homographies relating two adjacent trifocal tensors as well as the projection matrices depend linearly on the parameters two methods for estimating these parameters in a global way taking into account loops in the graph are developed both methods are based on sequential linear programming the first relies on a locally linear approximation of the polynomials involved in the loop constraints whereas the second uses alternating minimization both methods have the advantage of being non incremental and of uniformly distributing the error across all the cameras experiments carried out on several real data sets demonstrate the accuracy of the proposed approach and its efficiency in distributing errors over the whole set of cameras

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

application of sinc collocation method for solving a class of nonlinear fredholm integral equations in this paper the numerical solution of nonlinear fredholm integral equations of the second kind is considered by two methods the methods are developed by means of the sinc approximation with the single exponential se and double exponential de transformations these numerical methods combine a sinc collocation method with the newton iterative process that involves solving a nonlinear system of equations we provide an error analysis for the methods so far approximate solutions with polynomial convergence have been reported for this equation these methods improve conventional results and achieve exponential convergence some numerical examples are given to confirm the accuracy and ease of implementation of the methods

an efficient numerical scheme for a nonlinear integro differential equations with an integral boundary condition nonlinear functional integro differential equations with an integral boundary condition is appeared in chemical engineering underground water flow and population dynamics phenomena and other field of physics and mathematical chemistry so this paper presents a powerful numerical approach based on an iterative technique and sinc quadrature to estimate a solution for this equation then convergence of this technique is discussed by preparing a theorem which guarantees the applicability of that finally some numerical examples are given to confirm efficiency and accuracy of the numerical scheme

stochastic admissibility for a class of singular markovian jump systems with mode dependent time delays abstract this paper deals with the problem of the stochastic admissibility for a class of singular markovian jump systems with mode dependent time delays the singular matrices e r t in the considered systems are mode dependent based on the lyapunov functional method and the free weighting matrix method sufficient conditions are derived in terms of strict linear matrix inequalities lmis to guarantee the considered systems to be stochastically admissible numerical examples are provided to show the effectiveness of the proposed approaches

convergence analysis of sinc collocation methods for nonlinear fredholm integral equations with a weakly singular kernel in this paper the efficient methods are proposed for solving nonlinear fredholm integral equations with a weakly singular kernel by using sinc approximation with the single exponential se and double exponential de transformations the methods are developed sinc approximation has considerable advantages approximation by sinc functions handles singularities in the problem and such approximations yield rapidly convergent schemes for solving the problem furthermore convergence of proposed methods is discussed by preparing the theorems which show exponential convergence and guarantee the applicability of those finally some numerical examples are presented to illustrate efficiency and accuracy of the numerical schemes

h control of parameter dependent state delayed systems using polynomial parameter dependent quadratic functions this paper presents the issue of robust disturbance attenuation and robust asymptotic stability problem for finite dimensional linear parameter dependent state delayed systems the use of polynomial parameter dependent quadratic lyapunov functions and linear matrix inequalities lmis formulations for robust h control are considered it is shown that the state feedback control can be determined to guarantee the stability of the closed loop system independently of the time delay we present an illustrative example to demonstrate the applicability of the proposed design approach

error estimates with explicit constants for sinc approximation sinc quadrature and sinc indefinite integration error estimates with explicit constants are given for approximations of functions definite integrals and indefinite integrals by means of the sinc approximation although in the literature various error estimates have already been given for these approximations those estimates were basically for examining the rates of convergence and several constants were left unevaluated giving more explicit estimates i e evaluating these constants is of great practical importance since by this means we can reinforce the useful formulas with the concept of verified numerical computations in this paper we reveal the explicit form of all constants in a computable form under the same assumptions of the existing theorems the function to be approximated is analytic in a suitable region we also improve some formulas themselves to decrease their computational costs numerical examples that confirm the theory are also given

l2 l filter design for discrete time singular markovian jump systems with time varying delays the problem of l 2 l filter design for discrete time singular systems with markovian jump and time varying delays is investigated in this paper by using the delay partitioning technique a delay dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed l 2 l performance index based on the derived condition the full order and reduced order filters with mode independent characterization are designed in a unified framework the corresponding filter parameters can be obtained by solving a set of linear matrix inequalities the reported results not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism two numerical examples are provided to illustrate the effectiveness of the proposed methods

sinc collocation approximation of non smooth solution of a nonlinear weakly singular volterra integral equation a numerical method based on sinc collocation approximation for a class of nonlinear weakly singular volterra integral equations of a second kind with non smooth solution is given the numerical method given here combines a sinc collocation method with an explicit iterative process that involves solving a nonlinear system of equations we provide an error analysis for the method it is shown that the approximate solution converges to the exact solution at the rate of mexp cm where m is the number of collocation points and c is some positive constant some numerical results for several test functions are given to confirm the accuracy and the ease of implementation of the method

quadrature formulas obtained by variable transformation and the de rule abstract this paper gives a survey of the results known to date about quadrature formulas obtained by variable transformation followed by an application of the trapezoidal rule with an equal mesh size it has been shown that a formula obtained by an appropriate transformation is in general efficient and also robust against the end point singularity various kinds of useful transformations together with the asymptotic error behaviors of the resulting quadrature formulas are summarized in particular special emphasis is placed on an asymptotically optimal formula called the double exponential formula abbreviated as the de rule which is characterized by the double exponential decrease of its weights in the neighborhood of the end points of the transformed interval of integration

de sinc methods have almost the same convergence property as se sinc methods even for a family of functions fitting the se sinc methods in this paper the theoretical convergence rate of the trapezoidal rule combined with the double exponential de transformation is given for a class of functions for which the single exponential se transformation is suitable it is well known that the de transformation enables the rule to achieve a much higher rate of convergence than the se transformation and the convergence rate has been analyzed and justified theoretically under a proper assumption here it should be emphasized that the assumption is more severe than the one for the se transformation and there actually exist some examples such that the trapezoidal rule with the se transformation achieves its usual rate whereas the rule with de does not such cases have been observed numerically but no theoretical analysis has been given thus far this paper reveals the theoretical rate of convergence in such cases and it turns out that the de s rate is almost the same as but slightly lower than that of the se by using the analysis technique developed here the theoretical convergence rate of the sinc approximation with the de transformation is also given for a class of functions for which the se transformation is suitable the result is quite similar to above the convergence rate in the de case is slightly lower than in the se case numerical examples which support those two theoretical results are also given

an efficient solution to the five point relative pose problem an efficient algorithmic solution to the classical five point relative pose problem is presented the problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points the algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and subsequently finding its roots it is the first algorithm well suited for numerical implementation that also corresponds to the inherent complexity of the problem we investigate the numerical precision of the algorithm we also study its performance under noise in minimal as well as overdetermined cases the performance is compared to that of the well known 8 and 7 point methods and a 6 point scheme the algorithm is used in a robust hypothesize and test framework to estimate structure and motion in real time with low delay the real time system uses solely visual input and has been demonstrated at major conferences

robust stability and stabilization for singular systems with state delay and parameter uncertainty considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay the parametric uncertainty is assumed to be norm bounded the purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular impulse free and stable for all admissible uncertainties while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed loop system is robustly stable these problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization respectively necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived a strict linear matrix inequality lmi design approach is developed an explicit expression for the desired robust state feedback control law is also given finally a numerical example is provided to demonstrate the application of the proposed method

improved fuzzy control design for nonlinear markovian jump systems with incomplete transition descriptions this paper addresses the state feedback control of nonlinear continuous time markovian jump systems the nonlinearity is represented by takagi sugeno fuzzy models and the transition probability matrix is assumed to be partly known some elements in the matrix are known some are unknown but with known lower and upper bounds and some are completely unknown by making full use of the continuous property of the transition probability matrix new sufficient conditions for the stochastic stability of the system are obtained in terms of linear matrix inequalities we show that the conditions given are less conservative than or at least the same as those for existing results moreover using the conditions obtained we establish a method for design of a h state feedback controller numerical examples illustrate the effectiveness of the proposed method

symmetrization of the sinc galerkin method for boundary value problems on procede a la symetrisation de la methode de galerkin en modifiant la fonction poids pour une classe etendue de problemes aux valeurs limites

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

the double exponential sinc collocation method for singular sturm liouville problems sturm liouville problems are abundant in the numerical treatment of scientific and engineering problems in the present contribution we present an efficient and highly accurate method for computing eigenvalues of singular sturm liouville boundary value problems the proposed method uses the double exponential formula coupled with sinc collocation method this method produces a symmetric positive definite generalized eigenvalue system and has exponential convergence rate numerical examples are presented and comparisons with single exponential sinc collocation method clearly illustrate the advantage of using the double exponential formula

stabilization of singular markovian jump systems with generally uncertain transition rates this note is devoted to investigating the stability and stabilization problems for continuous time singular markovian jump systems smjss with generally uncertain transition rates gutrs in this gutr singular model each transition rate can be completely unknown or only its estimate value is known in terms of a set of coupled linear matrix inequalities lmis a sufficient condition is established to ensure the systems to be regular impulse free and stochastically stable moreover the corresponding sufficient condition on the existence of a mode dependent state feedback controller is derived to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method

error estimates with explicit constants for the sinc approximation over infinite intervals abstract the sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis even for other functions the sinc approximation works accurately when combined with a proper variable transformation the convergence rate has been analyzed for typical cases including finite semi infinite and infinite intervals recently for verified numerical computations a more explicit computable error bound has been given in the case of a finite interval in this paper such explicit error bounds are derived for other cases

motion estimation for nonoverlapping multicamera rigs linear algebraic and l geometric solutions we investigate the problem of estimating the ego motion of a multicamera rig from two positions of the rig we describe and compare two new algorithms for finding the 6 degrees of freedom 3 for rotation and 3 for translation of the motion one algorithm gives a linear solution and the other is a geometric algorithm that minimizes the maximum measurement error the optimal l solution they are described in the context of the general camera model gcm and we pay particular attention to multicamera systems in which the cameras have nonoverlapping or minimally overlapping field of view many nonlinear algorithms have been developed to solve the multicamera motion estimation problem however no linear solution or guaranteed optimal geometric solution has previously been proposed we made two contributions 1 a fast linear algebraic method using the gcm and 2 a guaranteed globally optimal algorithm based on the l geometric error using the branch and bound technique in deriving the linear method using the gcm we give a detailed analysis of degeneracy of camera configurations in finding the globally optimal solution we apply a rotation space search technique recently proposed by hartley and kahl our experiments conducted on both synthetic and real data have shown excellent results

near optimality of the sinc approximation near optimality of the sinc approximation is established in a variety of spaces of functions analytic in a strip region about the real axis each space being characterized by the decay rate of their elements functions in the neighborhood of the infinity

summary of sinc numerical methods sinc approximation methods excel for problems whose solutions may have singularities or infinite domains or boundary layers this article summarizes results obtained to date on sinc numerical methods of computation sinc methods provide procedures for function approximation over bounded or unbounded regions encompassing interpolation approximation of derivatives approximate definite and indefinite integration solving initial value ordinary differential equation problems approximation and inversion of fourier and laplace transforms approximation of hilbert transforms and approximation of indefinite convolutions the approximate solution of partial differential equations and the approximate solution of integral equations methods for constructing conformal maps and methods for analytic continuation indeed sinc are ubiquitous for approximating every operation of calculus

bayesian model estimation and selection for epipolar geometry and generic manifold fitting computer vision often involves estimating models from visual input sometimes it is possible to fit several different models or hypotheses to a set of data and a decision must be made as to which is most appropriate this paper explores ways of automating the model selection process with specific emphasis on the least squares problem of fitting manifolds in particular algebraic varieties e g lines algebraic curves planes etc to data points illustrated with respect to epipolar geometry the approach is bayesian and the contribution three fold first a new bayesian description of the problem is laid out that supersedes the author s previous maximum likelihood formulations this formulation will reveal some hidden elements of the problem second an algorithm mapsac is provided to obtain the robust map estimate of an arbitrary manifold third a bayesian model selection paradigm is proposed the bayesian formulation of the manifold fitting problem uncovers an elegant solution to this problem for which a new method gric for approximating the posterior probability of each putative model is derived this approximations bears some similarity to the penalized likelihoods used by aic bic and mdl however it is far more accurate in situations involving large numbers of latent variables whose number increases with the data this will be empirically and theoretically demonstrated

recent developments of the sinc numerical methods abstract this paper gives a survey of recent developments of the sinc numerical methods a variety of sinc numerical methods have been developed by stenger and his school for a certain class of problems the sinc numerical methods have the convergence rates of o exp n with some 0 where n is the number of nodes or bases used in the methods recently it has turned out that the sinc numerical methods can achieve convergence rates of o exp n log n with some 0 for a smaller but still practically meaningful class of problems and that these convergence rates are best possible the present paper demonstrates these facts for two sinc numerical methods the sinc approximation and the sinc collocation method for two point boundary value problems

the double exponential transformation in numerical analysis the double exponential transformation was first proposed by takahasi and mori in 1974 for the efficient evaluation of integrals of an analytic function with end point singularity afterwards this transformation was improved for the evaluation of oscillatory functions like fourier integrals recently it turned out that the double exponential transformation is useful not only for numerical integration but also for various kinds of sinc numerical methods the purpose of the present paper is to review the double exponential transformation in numerical integration and in a variety of sinc numerical methods

brief paper mode dependent h filtering for discrete time markovian jump linear systems with partly unknown transition probabilities in this paper the problem of h filtering for a class of discrete time markovian jump linear systems mjls with partly unknown transition probabilities is investigated the considered systems are more general which cover the mjls with completely known and completely unknown transition probabilities as two special cases a mode dependent full order filter is constructed and the bounded real lemma brl for the resulting filtering error system is derived via lmi formulation then an improved version of the brl is further given by introducing additional slack matrix variables to eliminate the cross coupling between system matrices and lyapunov matrices among different operation modes finally the existence criterion of the desired filter is obtained such that the corresponding filtering error system is stochastically stable with a guaranteed h performance index a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

exponential mean square stability of time delay singular systems with markovian switching and nonlinear perturbations abstract this paper considers exponential stability in mean square of singular markovian jump systems the systems under consideration involve nonlinear perturbation and time varying delays by using the lyapunov krasovskii functional delay dependent stability conditions in terms of linear matrix inequality lmi are addressed which guarantee exponential mean square stability and a prescribed h performance index for the considered systems two numerical examples are given to illustrate the effectiveness of the proposed main results

function classes for successful de sinc approximations the de sinc formulas resulting from a combination of the sinc approximation formula with the double exponential de transformation provide a highly efficient method for function approximation in many cases they are more efficient than the se sinc formulas which are the sinc approximation formulas combined with the single exponential se transformations function classes suited to the se sinc formulas have already been investigated in the literature through rigorous mathematical analysis whereas this is not the case with the de sinc formulas this paper identifies function classes suited to the de sinc formulas in a way compatible with the existing theoretical results for the se sinc formulas furthermore we identify alternative function classes for the de sinc formulas as well as for the se sinc formulas which are more useful in applications in the sense that the conditions imposed on the functions are easier to verify

transition probability bounds for the stochastic stability robustness of continuous and discrete time markovian jump linear systems this paper considers the robustness of stochastic stability of markovian jump linear systems in continuous and discrete time with respect to their transition rates and probabilities respectively the continuous time discrete time system is described via a continuous valued state vector and a discrete valued mode which varies according to a markov process chain by using stochastic lyapunov function approach and kronecker product transformation techniques sufficient conditions are obtained for the robust stochastic stability of the underlying systems which are in terms of upper bounds on the perturbed transition rates and probabilities analytical expressions are derived for scalar systems which are straightforward to use numerical examples are presented to show the potential of the proposed techniques

sinc approximation for numerical solution of integral equation arising in conductor like screening model for real solvent in this study we present the existence of solutions for some nonlinear integral equations known as hammerstein type which forms the basis for the conductor like screening model for real solvents cosmo rs by using the techniques of noncompactness measures we employ the basic fixed point theorems such as darbo s theorem to obtain the mentioned aim in banach algebra then this paper presents a powerful numerical approach based on the sinc approximation to solve the equation which forms the basis for the conductor like screening model for real solvents cosmo rs the approach is based on the recognition of the hammerstein integral equation for the determination of the chemical potential of a surface segment as a function of screening charge density then convergence of this technique is discussed by preparing a theorem which shows an exponential type convergence rate and guarantees the applicability of that

automatic camera calibration using multiple sets of pairwise correspondences we propose a new method to add an uncalibrated node into a network of calibrated cameras using only pairwise point correspondences while previous methods perform this task using triple correspondences these are often difficult to establish when there is limited overlap between different views in such challenging cases we must rely on pairwise correspondences and our solution becomes more advantageous our method includes an 11 point minimal solution for the intrinsic and extrinsic calibration of a camera from pairwise correspondences with other two calibrated cameras and a new inlier selection framework that extends the traditional ransac family of algorithms to sampling across multiple datasets our method is validated on different application scenarios where a lack of triple correspondences might occur addition of a new node to a camera network calibration and motion estimation of a moving camera inside a camera network and addition of views with limited overlap to a structure from motion model

optimality of the double exponential formula functional analysis approach in the light of the functional analysis theory we establish the optimality of the double exponential formula the argument consists of the following three ingredients 1 introduction of a number of spaces of functions analytic in a strip region about the real axis each space being characterized by the decay rate of their elements functions in the neighborhood of the infinity 2 proof of the near optimality of the trapezoidal formula in each space introduced in 1 by showing the near equality between an upper estimate for the error norm of the trapezoidal formula and a lower estimate for the minimum error norm of quadratures 3 nonexistence theorem for the spaces the characterizing decay rate of which is more rapid than the double exponential

de sinc methods have almost the same convergence property as se sinc methods even for a family of functions fitting the se sinc methods part ii indefinite integration in this paper the theoretical convergence rate of the sinc indefinite integration combined with the double exponential de transformation is given for a class of functions for which the single exponential se transformation is suitable although the de transformation is considered as an enhanced version of the se transformation for sinc related methods the function space for which the de transformation is suitable is smaller than that for se and therefore there exist some examples such that the de transformation is not better than the se transformation even in such cases however some numerical observations in the literature suggest that there is almost no difference in the convergence rates of se and de in fact recently the observations have been theoretically explained for two explicit approximation formulas the sinc quadrature and the sinc approximation the conclusion is that in such cases the de s rate is slightly lower but almost the same as that of the se the contribution of this study is the derivation of the same conclusion for the sinc indefinite integration numerical examples that support the theoretical result are also provided

double exponential transformation in the sinc collocation method for two point boundary value problems in 1974 takahasi and mori proposed the double exponential transformation for efficient evaluation of integrals of an analytic function with end point singularity recently it has turned out that the double exponential transformation is also useful for various kinds of sinc methods in the present paper we consider the sinc collocation method for two point boundary value problems to show that the method can be considerably enhanced when incorporated with the double exponential transformation technique