gauss quadrature rules for partial support and logarithmic singular integrals with compactly supported wavelets abstract wavelet gauss quadrature methods are effective approaches to evaluate the inner products with wavelets or with associated scaling functions by a lifting trick a barinka t barsch s dahlke et al some remarks on quadrature formulas for refinable functions and wavelets z angew math mech 81 12 2001 839 885 the compactly supported wavelets and the associated scaling functions can be used as weighted functions gauss quadrature rules for wavelets on partial support are obtained in this paper based on the wavelet moments and the partial moments formulas for calculating the logarithmic wavelet moments are introduced finally gauss quadrature rules with the product of scaling functions and logarithmic singular functions as the weight function are constructed the accuracy of the rules is illustrated by two numerical experiments

bernstein operators for extended chebyshev systems abstract let u n c n a b be an extended chebyshev space of dimension n 1 suppose that f 0 u n is strictly positive and f 1 u n has the property that f 1 f 0 is strictly increasing we search for conditions ensuring the existence of points t 0 t n a b and positive coefficients 0 n such that for all f c a b the operator b n c a b u n defined by b n f k 0 n f t k k p n k satisfies b n f 0 f 0 and b n f 1 f 1 here it is assumed that p n k k 0 n is a bernstein basis defined by the property that each p n k has a zero of order k at a and a zero of order n k at b

analysis of the energy based control for swinging up two pendulums this note studies the energy based control for swinging up two pendulums on a cart and it presents an original analysis of the convergence of the energy and the motion of the two pendulums for the two pendulums with the different natural frequencies irrespective of initial state of the two pendulums it is shown that the energy of each pendulum converges to either of two values and the motion of the two pendulums can be described by four invariant sets moreover the stability analysis of the motion of the two pendulums is performed via the concept of stability of an invariant set the results obtained in this note not only show theoretically the effectiveness of the energy based control for swinging up the two pendulums but also pave one way for analyzing and designing the energy based control for more complicated underactuated mechanical systems

on the multivariate horner scheme we present an efficient version of the horner scheme for the evaluation of multivariate polynomials and study its stability properties in particular we show that the backward error of evaluation is bounded by a quantity that is linear in the total degree of the polynomial which itself is usually significantly smaller than the number of operations involved in the evaluation process moreover we show that the same type of estimates holds also for the forward error provided that the polynomial basis is chosen suitably

a multiresolution approach to regularization of singular operators and fast summation singular and hypersingular operators are ubiquitous in problems of physics and their use requires a careful numerical interpretation although analytical methods for their regularization have long been known the classical approach does not provide numerical procedures for constructing or applying the regularized operator we present a multiresolution definition of regularization for integral operators with convolutional kernels which are homogeneous or associated homogeneous functions we show that our procedure yields the same operator as the classical definition moreover due to the constructive nature of our definition we provide concise numerical procedures for the construction and application of singular and hypersingular operators as an application we present an algorithm for fast computation of discrete sums and briefly discuss several other examples

a note on the optimal stability of bases of univariate functions this note is concerned with the characterizations and uniqueness of bases of finite dimensional spaces of univariate continuous functions which are optimally stable for evaluation with respect to bases whose elements have no sign changes

a new efficient method for cases of the singular integral equation of the first kind various cases of cauchy type singular integral equation of the first kind occur rather frequently in mathematical physics and possess very unusual properties these equations are usually difficult to solve analytically and it is required to obtain approximate solutions this paper investigates the numerical solution of various cases of cauchy type singular integral equations using reproducing kernel hilbert space rkhs method the solution u x is represented in the form of a series in the reproducing kernel space afterwards the n term approximate solution u n x is obtained and it is proved to converge to the exact solution u x the major advantage of the method is that it can produce good globally smooth approximate solutions moreover in this paper an efficient error estimation of the rkhs method is introduced finally numerical experiments show that our reproducing kernel method is efficient

log canonical thresholds and monge ampere masses in this paper we prove an inequality for log canonical thresholds and monge ampere masses the idea of proof is a combination of the ohsawa takegoshi l 2 extension theorem and inequalities in ahag et al adv math 222 2036 2058 2009 and demailly and pham acta math 212 1 9 2014

finding the zeros of a univariate equation proxy rootfinders chebyshev interpolation and the companion matrix when a function f x is holomorphic on an interval x in a b its roots on the interval can be computed by the following three step procedure first approximate f x on a b by a poly

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

evaluation of the derivative of a polynomial in bernstein form in geometric modelling and computer aided design a polynomial is usually represented in bernstein form forward error analysis for the computation of the derivative of a polynomial in bernstein form is performed the corresponding running error is also analyzed we have compared our results with those corresponding to a polynomial represented in power basis and using legendre and chebyshev forms since the conversions between the bernstein and the power bases and between bernstein and chebyshev polynomials were already studied in the literature for the sake of completeness the conversion between bernstein and chebyshev polynomials of the first kind is analyzed in an appendix

numerical solution of systems of cauchy singular integral equations with constant coefficients abstract this paper deals with the numerical solution of a class of systems of cauchy singular integral equations with constant coefficients the proposed procedure consists of two basic steps the first one is to consider a modified problem equivalent to the original one under suitable conditions the second one is to approximate its solution by means of a vector of polynomial functions such array is constructed by applying a quadrature type method based on gaussian rules that leads to solve a determined and well conditioned linear system the convergence and stability of the method are proved in weighted l 2 spaces some numerical tests are also shown

approximate solution of a class of singular integral equations of second kind a simple method based on polynomial approximation of a function is employed to obtain approximate solution of a class of singular integral equations of the second kind for a hypersingular integral equation of the second kind this method avoids the complex function theoretic method and produces the known exact solution to prandtl s integral equation as a special case for a particular singular integro differential equation of the second kind this also produces an approximate solution which compares favourably with numerical results obtained by various galerkin methods the convergence of the method for both the equations is also established

non normal type singular integral differential equations by riemann hilbert approach abstract this article deals with one class of singular integral differential equations of non normal type with convolution and cauchy principal value integral in class 0 by using fourier transform this classes of equations are transformed into a riemann boundary value problem with nodal point and we prove the existence of solutions and the noether theory for the equations for such equations we propose one method different from classical one and we obtain the general solutions and the conditions of solvability all cases about the behaviors of the solution are considered at nodal points therefore the theory of integral equations and the classical riemann boundary value problems is extended further

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

on the definition of the monge ampere operator in ℂ 2 we show that if u is a plurisubharmonic function defined on an open subset of 2 then the monge ampere measure dd cu 2 can be well defined if and only if u belongs to the sobolev space w 1 2 loc

on the consistency of numerical solutions of singular integral equations of the second kind with negative index using jacobi polynomials abstract singular integral equations of second kind with negative index possess bounded solutions whenever the forcing function satisfies the orthogonality conditions numerically the discretization of the integrals via gauss jacobi quadrature does not ensure the preservation of a consistent system it is shown that for gauss jacobi quadrature the overdetermined system of equations is consistent if and only if the discretized compatibility condition is satisfied the solutions of inconsistent systems via generalized inverses are considered error estimates are established which are shown to be independent of which equation is excluded in the solution of the overdetermined system

domains of definition of monge ampere operators on compact kahler manifolds let x be a compact kahler manifold we introduce and study the largest set dma x of plurisubharmonic psh functions on which the complex monge ampere operator is well defined it is much larger than the corresponding local domain of definition though still a proper subset of the set psh x of all psh functions we prove that certain twisted monge ampere operators are well defined for all psh functions as a consequence any psh function with slightly attenuated singularities has finite weighted monge ampere energy

deriving the continuity of maximum entropy basis functions via variational analysis in this paper we prove the continuity of maximum entropy basis functions using variational analysis techniques the use of information theoretic variational principles to derive basis functions is a recent development in this setting data approximation is viewed as an inductive inference problem with the basis functions being synonymous with a discrete probability distribution and the polynomial reproducing conditions acting as the linear constraints for a set of distinct nodes x i i 1 n in mathbb r d the convex approximation of a function u x is u h x sum i 1 n p i x u i where p i i 1 n are nonnegative basis functions and u h x must reproduce affine functions sum i 1 n p i x 1 sum i 1 n p i x x i x given these constraints we compute p i x by minimizing the relative entropy functional kullback leibler distance d p m sum i 1 n p i x ln p i x m i x where m i x is a known prior weight function distribution to prove the continuity of the basis functions we appeal to the theory of epiconvergence

the runge example for interpolation and wilkinson s examples for rootfinding we look at two classical examples in the theory of numerical analysis namely the runge example for interpolation and wilkinson s example actually two examples for rootfinding we use the modern

approximate model predictive control laws for constrained nonlinear discrete time systems analysis and offline design the objective of this work consists in the offline approximation of possibly discontinuous model predictive control laws for nonlinear discrete time systems while enforcing hard constraints on state and input variables obtaining an offline approximation of the receding horizon control law may lead to a very significant reduction of the online computational burden with respect to algorithms based on iterated optimization thus allowing the application to fast dynamics plants the proposed approximation scheme allows to cope with discontinuous control laws such as those arising from constrained nonlinear finite horizon optimal control problems a detailed stability analysis of the closed loop system driven by the approximated state feedback controller shows that the devised technique guarantees the input to state practical stability with respect to the non fading approximation induced errors two examples are provided to show the effectiveness of the method when the approximator is chosen either as a d

an approximate numerical method for solving cauchy singular integral equations composed of multiple implicit parameter functions with unknown integral limits in contact mechanics abstract cauchy singular integral equations are widely used in physics and mathematics especially in solid contact mechanics the solution of cauchy singular integral equations composed of explicit functions has already been achieved in existing research however when dealing with the contact problem between two solid bodies with irregular surfaces described by implicit parametric functions difficulties arise when trying to solve the cauchy singular integral because it is composed of multiple implicit parameter functions moreover the integral limits are unknown and constrained by physical characteristics to solve this kind of problem an approximate calculation method with high accuracy will be provided in this paper specifically based on the quadrature method and taking the constraint function of the boundary as the convergence criterion both the integral limits satisfying the physical characteristics condition and the solution of the cauchy singular integral equations composed of multiple parameter functions can be derived by an iterative method finally five different examples are calculated using the new method and the absolute errors between the approximate values provided by the new method and the true values are analysed

an observer based controller for nonlinear systems a gain scheduling approach abstract this paper presents an observer based controller for discrete time nonlinear systems whose control inputs are subject to a set of equality and or inequality constraints firstly a regularized least square estimator is developed to estimate the states of the nonlinear system then the estimated states are used to generate a feedback control law using the jacobean linearization in conjunction with gain scheduling the stability of the closed loop control system is rigorously investigated applications of the proposed observer based control scheme to two numerical examples are presented then the developed controller is used to control a synchronous machine which is subject to constraints on the control the simulation results show the effectiveness of the proposed observer based control scheme

solving singular integral equations using gaussian quadrature and overdetermined systems abstract for singular integral equations of the cauchy type on an open interval a bounded solution exists only if an additional condition is satisfied in direct methods of solution when the integrals are replaced by quadratures it is not obvious that the resulting discrete system of equations will be consistent it is shown that for gauss chebyshev quadrature the overdetermined system of equations is consistent if and only if the discrete analog of the compatibility condition is satisfied the behavior of solutions to inconsistent systems is examined

the solvability and explicit solutions of singular integral differential equations of non normal type via riemann hilbert problem abstract in this article we study non normal type singular integral differential equations involving convolution kernel and cauchy kernel in class 0 and we prove the existence of solutions and the noether conditions by using theory of fourier analysis the equations under consideration are transformed into boundary value problems for analytic functions i e riemann hilbert problems with discontinuous coefficients for such problems we propose one method different from classical one and we obtain the analytic solutions and the conditions of noether solvability at nodal points all cases as regards the regularity and the asymptotic behaviors of the solution are discussed in detail in particular we generalize the case of normal type discussed in the literature li 2017 7 8 2020 2019 to the case of non normal type

barrier lyapunov functions for the output tracking control of constrained nonlinear switched systems abstract in this paper we investigate the output tracking control problem of constrained nonlinear switched systems in lower triangular form first when all the states are subjected to constraints we employ a barrier lyapunov function blf which grows to infinity whenever its arguments approach some finite limits to prevent the states from violating the constraints based on the simultaneous domination assumption we design a continuous feedback controller for the switched system which guarantees that asymptotic output tracking is achieved without transgression of the constraints and all closed loop signals remain bounded provided that the initial states are feasible then we further consider the case of asymmetric time varying output constraints by constructing an appropriate blf finally the effectiveness of the proposed results is demonstrated with a numerical example

a comparison principle for the complex monge ampere operator in cegrell s classes and applications in this article we will first prove a result about the convergence in capacity next we will obtain a general decomposition theorem for complex monge ampere measures which will be used to prove a c

on the optimal stability of the bernstein basis we show that the bernstein polynomial basis on a given interval is optimally stable in the sense that no other nonnegative basis yields systematically smaller condition numbers for the values or roots of arbitrary polynomials on that interval this result follows from a partial ordering of the set of all nonnegative bases that is induced by nonnegative basis transformations we further show by means of some low degree examples that the bernstein form is not uniquely optimal in this respect however it is the only optimally stable basis whose elements have no roots on the interior of the chosen interval these ideas are illustrated by comparing the stability properties of the power bernstein and generalized ball bases

cauchy singular integral equations in spaces of continuous functions and methods for their numerical solution cauchy singular integral equations on an interval are studied in weighted spaces of continuous functions convergence rates for a general method for their numerical solution are proved in weighted uniform norms applications of these results to the collocation method and the quadrature method are given

generalized convolution type singular integral equations in this paper we study one class of generalized convolution type singular integral equations in class 0 such equations are turned into complete singular integral equations with nodal points and further turned into boundary value problems for analytic function with discontinuous coefficients by fourier transforms for such equations we will propose one method different from classical one and obtain the general solutions and their conditions of solvability in class 0 thus this paper generalizes the theory of classical equations of convolution type

the domain of definition of the complex monge ampere operator we give a precise characterization of those plurisubharmonic functions for which one can well define the monge ampere operator as a regular borel measure

a companion matrix resultant for bernstein polynomials abstract a closed form expression for a companion matrix m of a bernstein polynomial is obtained and this is used to derive an expression for a resultant matrix of two bernstein polynomials it is shown that m differs from its equivalent form for a power basis polynomial because an upper triangular hankel matrix does not define a similarity transformation between m and m t a measure of the numerical condition of a resultant matrix for polynomials in an arbitrary basis is reviewed and this is used to compare the stability of two resultant matrices in particular computational tests are performed and it is shown that the resultant matrix of two bernstein polynomials is numerically better conditioned than the resultant matrix that is obtained when a simple parameter substitution is used to transform the polynomials to the power basis

continuity of the complex monge ampere operator on compact kahler manifolds we prove several approximation theorems of the complex monge ampere operator on a compact kahler manifold as an application we prove the cegrell type theorem on a complete description of the range of the complex monge ampere operator in the class of plurisubharmonic functions with vanishing complex monge ampere mass on all pluripolar sets as a by product we obtain a stability theorem of solutions of complex monge ampere equations

solvability of singular integro differential equations via riemann hilbert problem abstract the article is to study singular integro differential equations involving convolutional operators and cauchy integral operators via riemann hilbert problem to do this we adopt a new approach through fourier transform on l 2 subspace which is holder continuous with a certain decay at infinity the fourier transform converts the equations into a riemann hilbert problem with holder continuous coefficients and with nodal points which allows us to construct the general solutions

a collocation scheme for a certain cauchy singular integral equation based on the superconvergence analysis in this paper we investigate the composite midpoint rule for the evaluation of cauchy principal value integral in an interval and place the key point on its pointwise superconvergence phenomenon the error expansion of the rule is obtained which shows that the superconvergence phenomenon occurs at the points of each subinterval whose local coordinate is the zeros of some function then by applying the midpoint rule to approximate the cauchy principal value integral and choosing the superconvergence points as the collocation points we obtain a collocation scheme for solving a certain cauchy singular integral equation the more interesting thing is that the coefficient matrix of the resulting linear system possesses some good properties from which we obtain an optimal error estimate finally some numerical examples are provided to validate the theoretical analysis

shape preserving properties of generalized bernstein operators on extended chebyshev spaces we study the existence and shape preserving properties of a generalized bernstein operator b n fixing a strictly positive function f 0 and a second function f 1 such that f 1 f 0 is strictly increasing within the framework of extended chebyshev spaces u n the first main result gives an inductive criterion for existence suppose there exists a bernstein operator b n c a b u n with strictly increasing nodes fixing f 0 f 1 in u n if u n subset u n 1 and u n 1 has a non negative bernstein basis then there exists a bernstein operator b n 1 c a b u n 1 with strictly increasing nodes fixing f 0 and f 1 in particular if f 0 f 1 f n is a basis of u n such that the linear span of f 0 f k is an extended chebyshev space over a b for each k 0 n then there exists a bernstein operator b n with increasing nodes fixing f 0 and f 1 the second main result says that under the above assumptions the following inequalities hold b n f geq b n 1 f geq f furthermore b nf is f0 f1 convex for all f0 f1 convex functions f in c a b

rational cubic clipping with linear complexity for computing roots of polynomials many problems in computer aided geometric design and computer graphics can be turned into a root finding problem of polynomial equations among various clipping methods the ones based on the bernstein bezier form have good numerical stability one of such clipping methods is the k clipping method where k 2 3 and often called a cubic clipping method when k 3 it utilizes o n2 time to find two polynomials of degree k bounding the given polynomial f t of degree n and achieves a convergence rate of k 1 for a single root the roots of the bounding polynomials of degree k are then used for bounding the roots of f t this paper presents a rational cubic clipping method for finding two bounding cubics within o n time which can achieve a higher convergence rate 5 than that of 4 of the previous cubic clipping method when the bounding cubics are obtained the remaining operations are the same as those of previous cubic clipping method numerical examples show the efficiency and the convergence rate of the new method

clenshaw curtis type quadrature rule for hypersingular integrals with highly oscillatory kernels abstract the clenshaw curtis type quadrature rule is proposed for the numerical evaluation of the hypersingular integrals with highly oscillatory kernels and weak singularities at the end points for any smooth functions g x based on the fast hermite interpolation this paper provides a stable recurrence relation for these modified moments convergence rates with respect to the frequency k and the number of interpolation points n are considered these theoretical results and high accuracy of the presented algorithm are illustrated by some numerical examples

numerical solution of some classes of integral equations using bernstein polynomials this paper is concerned with obtaining approximate numerical solutions of some classes of integral equations by using bernstein polynomials as basis the integral equations considered are fredholm integral equations of second kind a simple hypersingular integral equation and a hypersingular integral equation of second kind the method is explained with illustrative examples also the convergence of the method is established rigorously for each class of integral equations considered here

uniqueness in e x ω abstract we prove uniqueness for the dirichlet problem for the complex monge ampere equation on compact kahler manifolds in the case of probability measures vanishing on pluripolar sets the proof uses the mass concentration technique due to kolodziej coupled with inequalities for mixed monge ampere measures and the comparison principle

the weighted monge ampere energy of quasiplurisubharmonic functions abstract we study degenerate complex monge ampere equations on a compact kahler manifold x we show that the complex monge ampere operator d d c n is well defined on the class e x of plurisubharmonic functions with finite weighted monge ampere energy the class e x is the largest class of psh functions on which the monge ampere operator is well defined and the comparison principle is valid it contains several functions whose gradient is not square integrable we give a complete description of the range of the operator d d c n on e x as well as on some of its subclasses we also study uniqueness properties extending calabi s result to this unbounded and degenerate situation and we give applications to complex dynamics and to the existence of singular kahler einstein metrics

montonicity preservation on triangles it is well known that bernstein polynomials on triangles preserve monotonicity in this paper we define and study three kinds of monotonicity preservation of systems of bivariate functions on a triangle we characterize and compare several of these systems and derive some geometric applications

signal and image approximation using interval wavelet transform in signal approximation classical wavelet synthesis are known to produce gibbs like phenomenon around discontinuities when wavelet coefficients in the cone of influence of the discontinuities are quantized by analyzing a function in a piecewise manner filtering across discontinuities can be avoided using this principle the interval wavelet transform can generate sparser representations in the vicinity of discontinuities than classical wavelet transforms this work introduces two new constructions of interval wavelets and shows how they can be used for image compression and upscaling

numerical solution for system of cauchy type singular integral equations with its error analysis in complex plane abstract in this paper the problem of finding numerical solution for a system of cauchy type singular integral equations of first kind with index zero is considered the analytic solution of such system is known but it is of limited use as it is a nontrivial task to use it practically due to the presence of singularity in the known solution itself therefore a residual based galerkin method is proposed with legendre polynomials as basis functions to find its numerical solution the proposed method converts the system of cauchy type singular integral equations into a system of linear algebraic equations which can be solved easily further hadamard conditions of well posedness are established for system of cauchy singular integral equations as well as for system of linear algebraic equations which is obtained as a result of approximation of system of singular integral equations with cauchy kernel the theoretical error bound is derived which can be used to obtain any desired accuracy in the approximate solution of system of cauchy singular integral equations the derived theoretical error bound is also validated with the help of numerical examples

on the numerical treatment of the singular integral equation of the second kind here a numerical treatment for solving the integral equation of the second kind with cauchy kernel is presented the singular term has been removed and the solution in the legendre polynomial form has been used to obtain a system of linear algebraic equation this system is solved numerically

solution of second kind integral equation with cauchy type kernel using daubechies scale function a method based on the daubechies scale function has been devised to solve numerically a class of second kind integral equations with a cauchy type kernel the convergence associated to the method has been established the method is illustrated with integral equations in this class whose exact solutions are known the numerical results obtained by the present method are seen to differ negligibly from the exact results

modified jacobi bernstein basis transformation and its application to multi degree reduction of bezier curves this paper reports new modified jacobi polynomials mjps we derive the basis transformation between mjps and bernstein polynomials and vice versa this transformation is merging the perfect least square performance of the new polynomials together with the geometrical insight of bernstein polynomials the mjps with indexes corresponding to the number of endpoints constraints are the natural basis functions for least square approximation of bezier curves using mjps leads us to deal with the constrained jacobi polynomials and the unconstrained jacobi polynomials as orthogonal polynomials the mjps are automatically satisfying the homogeneous boundary conditions thereby the main advantage of using mjps in multi degree reduction of bezier curves on computer aided geometric design cagd is that the constraints in cagd are also satisfied and that decreases the steps of multi degree reduction algorithm several numerical results for the multi degree reduction of bezier curves on cagd are given we establish and prove the basis transformation between the modified jacobi polynomials mjps and bernstein polynomials and vice versa this transformation is merging the perfect least square performance of the mjps with the geometrical insight of the bernstein form the mjps with indexes corresponding to the number of endpoint constraints are the natural basis functions for least square approximation of bezier curves several numerical results are considered

numerical approximation of 2d fredholm integral eigenvalue problems by orthogonal wavelets we investigate the numerical approximation of two dimensional second kind fredholm integral eigenvalue problems by the galerkin method with the cohen daubechies vial cdv wavelet family this choice provides us orthogonal bases for bounded domains avoiding the need of periodization or domain truncation the cdv family is indexed by the number of vanishing moments which drives the regularity of the basis we generate the galerkin basis from tensorized scaling functions and employ weighted gaussian quadratures derived from refinement equations numerical experiments address the relative computational cost of this approach with respect to the haar basis and the relationship between convergence rate and number of vanishing moments

a corner cutting algorithm for evaluating rational bezier surfaces and the optimal stability of the basis the usual method for evaluating rational bezier surfaces uses the projection operator and the representation provided by the bernstein basis we prove the optimal stability of the basis used in this representation we also propose an alternative method for evaluating rational surfaces through that representation we show the stability properties of this last method and prove that it has better properties than other known methods from the point of view of avoiding underflow and overflow

the computation of wavelet galerkin approximation on a bounded interval this paper describes exact evaluations of various finite integrals whose integrands involve products of daubechies compactly supported wavelets and their derivatives and or integrals these finite integrals play an essential role in the wavelet galerkin approximation of differential or integral equations on a bounded interval

an inequality for mixed monge ampere measures we generalize an inequality for mixed monge ampere measures from kolodziej indiana univ math j 43 1321 1338 1994 we also give an example that shows that our assumptions are sharp the corresponding result in the setting of compact kahler manifold is also discussed

legendre bernstein basis transformations abstract the bernstein form of a polynomial offers valuable insight into its geometrical behavior and has thus won widespread acceptance as the basis for bezier curves and surfaces for least squares approximation problems on the other hand the use of orthogonal bases such as the legendre polynomials permits simple and efficient constructions for convergent sequences of approximants we derive the transformation matrices that map the bernstein and legendre forms of a degree n polynomial on 0 1 into each other and examine the stability of this linear map in the p 1 and norms the condition number of the legendre bernstein transformation matrix grows at a significantly slower rate with n than in the well studied power bernstein case and at a dramatically slower rate than for other common e g bernstein hermite or power hermite basis conversions the utility of legendre representations in approximation problems and their relatively stable transformation to bernstein bezier form argue for more widespread applications of legendre methods in cagd algorithms

a new efficient method with error analysis for solving the second kind fredholm integral equation with cauchy kernel the main objective of this paper is to give an efficient numerical method for the solution of the second kind fredholm integral equation with cauchy type kernel although numerical treatment of singular integral equations sies has been considered by many researchers and many numerical methods have been proposed for the solution of this equation strong singularity of the cauchy singular integral operator still remains as a challenge to numerical methods most of the previous methods rely on specific quadrature rule or suitable base functions for capturing the singularity here we focus on operator transformation and graded mesh in addition we study error analysis in this regard efficiency of reproducing kernel hilbert space rkhs method using smooth transformation on the graded mesh is improved and compared with some other numerical methods

local property of the class eχ loc abstract in this paper we introduce a new weighted energy class of plurisubharmonic functions and show the local property of this class under some extra assumptions on weights

brief paper swing up and stabilization of a twin pendulum under state and control constraints by a fast nmpc scheme in this paper a real time implementable nonlinear model predictive control scheme is proposed for the swing up and the stabilization of a twin pendulum system under control and state constraints the basic feature lies in a particular parametrization of the set of candidate control profiles leading to a decision variable that may take only 3 admissible values simulations are proposed to assess the efficiency of the proposed feedback

application of jacobi polynomials to approximate solution of a singular integral equation with cauchy kernel abstract in this paper exact solution of the characteristic equation with cauchy kernel on the interval 1 1 is presented next jacobi polynomials are used to derive approximate solutions of the characteristic and general cauchy type singular integral equations moreover estimations of errors of the approximated solutions are presented and proved

condition numbers for singular integral equations in weighted l 2 spaces the convergence and stability of a discrete collocation method for cauchy singular integral equations in some weighted besov spaces are studied this numerical method results in solving a linear system in order to determine the unknown coefficients of the approximate solution the author proves that this linear system is well conditioned

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

singular integral equations of convolution type with cauchy kernel in the class of exponentially increasing functions abstract in this paper we study some classes of generalized singular integral equations of convolution type with cauchy kernel in the class of exponentially increasing functions such equations can be transformed into riemann boundary value problems with two unknown functions on two parallel straight lines via fourier transformation the general solutions and the conditions of solvability are obtained by means of the classical boundary value theory of the theory of fourier analysis and of the principle of analytic continuation this paper will be of great significance for the study of improving and developing complex analysis integral equation and boundary value problem therefore the classic riemann boundary value problem is extended further

numerical solution of a singular integro differential equation this paper presents a method based on polynomial approximation using bernstein polynomial basis to obtain approximate numerical solution of a singular integro differential equation with cauchy kernel the numerical results obtained by the present method compares favorably with those obtained by various galerkin methods earlier in the literature also the convergence of the method is established rigorously for the studied integro differential equation

nystrom method for cauchy singular integral equations with negative index in this paper the authors propose a nystrom method to approximate the solutions of cauchy singular integral equations with constant coefficients having a negative index they consider the equations in spaces of continuous functions with weighted uniform norm they prove the stability and the convergence of the method and show some numerical tests that confirm the error estimates

b splines and optimal stability it is proved that among all nonnegative bases of its space the b spline basis is optimally stable for evaluating spline functions

solvability theory of convolution singular integral equations via riemann hilbert approach abstract in this paper we study the solvability for some classes of singular integral equations of convolution type with discontinuous property in class 0 though such equations can be solved by using the classical bekya regularization method we are to give a new sectionally jumping method that is they may be reduced to boundary value problems of holomorphic functions which can be systematically solved and easily discussed we obtain the general solutions and the conditions of their solvability thus this paper generalizes the classical theory of integral equations

numerical solution of various cases of cauchy type singular integral equation abstract in this paper a robust but very simple numerical method is developed to solve various cases of cauchy type singular integral equation for this first bernstein polynomials are defined which are used for approximation of solution of the given singular integral equation then numerical method is introduced by using bernstein polynomials this ultimately leads to solution of a system of linear algebraic equations examples are illustrated to demonstrate simplicity of proposed method results are also compared with those present in literature to claim better efficiency of the method introduced

a fast algorithm for solving the generalized airfoil equation abstract the present paper is devoted to the quadrature method for cauchy type singular integral equations on 1 1 with an additional logarithmic singularity of the kernel an algorithm being based on this method is given whose realization only requires a computational work of o n ln n operations in order to determine n unknown coefficients of the approximate solution furthermore in a scale of weighted sobolev like spaces on 1 1 having analogous properties like the classical sobolev spaces on the unit circle the order of convergence is optimal

gauss quadrature rules for cauchy principal value integrals with wavelets gauss quadrature rules for cauchy principal value integrals with wavelets are established by the construction of orthogonal polynomials of wavelets and scaling functions as weight functions the wavelet gauss quadrature formulae for cauchy principal value integrals are introduced numerical examples are also presented

explicit solution of the finite time l2 norm polynomial approximation problem abstract the aim of this paper is to present a new approach to the finite time l 2 norm polynomial approximation problem a new formulation of this problem leads to an equivalent linear system whose solution can be investigated analytically such a solution is then specialized for a polynomial expressed in terms of laguerre and bernstein basis

a note on one point quadrature formula for daubechies scale function with partial support abstract this note is concerned with an efficient computation of integrals of products of a smooth function and daubechies scale function with partial support by using a one point quadrature rule the error estimate is obtained the rule is illustrated by considering an example from the literature

numerical solutions of cauchy singular integral equations using generalized inverses solving singular integral equations of cauchy type numerically involves solution of a linear system of equations the number of collocation and quadrature points decides the size of the linear system and an n n matrix is derived in most cases taking more collocation points may yield more accurate numerical solutions as in 1 and numerical difficulties arising in solving overdetermined system we show that the coefficient matrix of the overdetermined system obtained by taking more collocation points than quadrature nodes have the generalized inverse