construction of square root factor for solution of the lyapunov matrix equation abstract the lyapunov matrix equation is considered in this paper where the solution is a nonnegative definite matrix i e a matrix admitting decomposition in square root factors an algorithm for findings the square root factor without preliminary finding the solution itself is given

similarities of the integral pade approximants ii in this paper we show further similarities of the integral pade approximant the similarity of the integral pade approximant with the functional pade approximant and the improved functional epsilon algorithms is demonstrated the purpose of demonstrating the similarity between the integral pade approximant and the functional pade approximant is to verify our conjecture which is the integral pade approximant and the hybrid functional pade approximant produce identical rational functions finally we demonstrate the improvement of the classical functional epsilon algorithms which also has a relationship with the integral pade approximant

continued fractions and the potential models of confinement reply to a comment the analytic continued fractional formula for energies of the bound states in the harmonium potential v r ar 1 br cr2 as suggested by singh et al 1978 1979 and criticised by flessas 1982 is correct if and only if b 0 this is the special case of the more general result the author extends the analytic construction of the green function and the rigorous specification of its validity to the whole class of potentials with r2v r polynomial in ralpha alpha positive rational number

on the convergence of rows of vector pade approximants we state and prove a de montessus like theorem for vector valued meromorphic functions using vector pade approximants which are defined in the context of clifford algebras the proof is based on that used by saff for the scalar case the theorem may be regarded as an answer to a general problem posed by graves morris and saff

analytic approximations to kelvin functions with applications to electromagnetics we present analytical approximations for the real kelvin function ber x and the imaginary kelvin function bei x using the two point quasi fractional approximation procedure we have applied these approximations to the calculation of the current distribution within a cylindrical conductor our approximations are simple and accurate an infinite number of roots is also obtained with the approximation and precision increases with the value of the root our results could find useful applications in problems where analytical approximations of the kelvin functions are needed

a relaxed extragradient like method for a generalized mixed equilibrium problem a general system of generalized equilibria and a fixed point problem abstract very recently takahashi and takahashi s takahashi w takahashi strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a hilbert space nonlinear anal 69 2008 1025 1033 suggested and analyzed an iterative method for finding a common solution of a generalized equilibrium problem and a fixed point problem of a nonexpansive mapping in a hilbert space in this paper based on takahashi takahashi s iterative method and well known extragradient method we introduce a relaxed extragradient like method for finding a common solution of a generalized mixed equilibrium problem a general system of generalized equilibria and a fixed point problem of a strictly pseudocontractive mapping in a hilbert space and then obtain a strong convergence theorem utilizing this theorem we establish some new strong convergence results in fixed point problems variational inequalities mixed equilibrium problems and systems of generalized equilibria

clifford algebras and vector valued rational forms i we demonstrate how the use of clifford algebras in the theory of vector valued rational forms leads to practical recurrence relations which do not involve representations of the algebras

computable bounds for the sensitivity of the algebraic riccati equation in control or estimation theory linear quadratic optimization problems give rise to the so called matrix algebraic riccati equation are for such problems a crucial issue is the existence and uniqueness of a symmetric nonnegative definite stabilizing solution to the are and conditions on the equation parameters are known which guarantee both however in the context of computations in finite precision arithmetic and with imperfect parameter identification it is of concern whether the are retains such a solution in the proximity of a given set of parameters and how sensitive this solution is to parameter variation in this paper topological properties such as openness of the domain of existence and continuity with respect to parameters are established for the symmetric nonnegative definite stabilizing solution computable sensitivity estimates are also derived which quantitatively define a region of safe computation in terms of the parameters of the equation

an extension of a row convergence theorem for vector pade approximants abstract a row convergence theorem of de montessus type is established for vector pade approximants to a vector valued meromorphic function f while in a previous paper the authors established such a theorem for the case when f has simple poles the essential feature of the present paper is to treat the situation when f has multiple poles

nonlinear complementarity problem and galerkin method etude du probleme de complementarite non lineaire dans des espaces de dimensions infinies en utilisant l approximation de galerkin et une generalisation de l hypothese de karamardian on obtient plusieurs resultats d existence pour une forme speciale du probleme ou f x x l x t x l etant un operateur lineaire et t un operateur non lineaire

row convergence theorems for generalised inverse vector valued pade approximants abstract the approximants mentioned in the title are related to vector valued continued fractions and the vector algorithm devised by wynn in 1963 here we establish a unitary invariance property of these approximants and describe how the classical 1 dimensional pade approximants can be obtained as a special case the main results of the paper consist of de montessus de ballore type convergence theorems for row sequences having fixed denominator degree of vector valued approximants to meromorphic vector functions

generalized nonlinear variational inequalities abstract in this paper we investigate the existence results of solutions for a class of generalized nonlinear variational inequalities gnvi with nonmonotone set valued operators defined on noncompact sets in locally convex hausdorff topological vector spaces results that generalize the corresponding recent results of chang and zhang are derived

eigenvalues of the schrodinger equation with coulomb potentials plus linear and harmonic radial terms analytic approximations for the eigenvalues have been obtained using the two point quasifractional approximants method here we extend and generalize previous work where the method was applied to determine eigenenergies of two dimensional coulomb potentials in the presence of a magnetic field of arbitrary strength we have also shown the advantage of our results with respect to other calculations using the shifted 1 n method or pade approximants

computation of system balancing transformations and other applications of simultaneous diagonalization algorithms an algorithm is presented in this paper for computing state space balancing transformations directly from a state space realization the algorithm requires no squaring up or unnecessary matrix products various algorithmic aspects are discussed in detail a key feature of the algorithm is the determination of a contragredient transformation through computing the singular value decomposition of a certain product of matrices without explicitly forming the product other contragredient transformation applications are also described it is further shown that a similar approach may be taken involving the generalized singular value decomposition to the classical simultaneous diagonalization problem these svd based simultaneous diagonalization algorithms provide a computational alternative to existing methods for solving certain classes of symmetric positive definite generalized eigenvalue problems

about the newton iteration for spectral factorization abstract it is shown that theorem 1 2 of willems operators systems and linear algebra kaiserslautern 1997 european consort math indust jeubner stuggart 1997 pp 214 223 is analog of the outcomes of the statement 5 aliev and lorin systems contr lett 21 1993 485 491

variational inequalities with generalized monotone operators we investigate the variational inequality with pseudomonotone operators in the sense of karamardian in banach spaces new existence results which extend many known results in infinite dimensional spaces are derived under rather weak assumptions new uniqueness results which also seem to be new even in finite dimensional spaces are also derived in particular new existence and uniqueness results for the complementarity problem with pseudomonotone operators in banach spaces are obtained also existence and uniqueness results for minimization problems with pseudoconvex functions in banach spaces are obtained

the asymptotic iteration method for the eigenenergies of the schrodinger equation with the potential v r z r gr λr2 the eigenenergies of the schrodinger equation with coulomb potential plus linear and harmonic radial terms are investigated using the perturbation technique within the framework of the asymptotic iteration method the obtained eigenenergies are compared with those obtained from the shifted 1 n expansion method the moment method and also with the exact values obtained from the super symmetric method it is found that asymptotically this method gives accurate results for arbitrary g z and

a grassmann integral equation the present study introduces and investigates a new type of equation which is called grassmann integral equation in analogy to integral equations studied in real analysis a grassmann integral equation is an equation which involves grassmann berezin integrations and which is to be obeyed by an unknown function over a finite dimensional grassmann algebra gm i e a sought after element of the grassmann algebra gm a particular type of grassmann integral equations is explicitly studied for certain low dimensional grassmann algebras the choice of the equation under investigation is motivated by the effective action formalism of lattice quantum field theory in a very general setting for the grassmann algebras g2n n 2 3 4 the finite dimensional analogues of the generating functionals of the green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations finally by imposing the condition g g0 const 0 r k k k 1 n are the generat

higher order two point quasi fractional approximations to the bessel functions j o x and j 1 x on cherche des solutions approchees pour les fonctions de bessel j x 0 1 valables pour des valeurs de x petites et grandes

problems and progress in vector pade approximation abstract some open problems in vector pade approximation are stated and some recent de montessus type theorems governing convergence of rows of the vector pade table are contrasted weshow how these results indicate when it is more appropriate to use generalised inverse vector pade approximants or their hybridised form we show how a straightforward analogue of the berlekamp massey algorithm may be used to calculate generalised inverse vector pade approximants this algorithm is applied to the derivation of a new low order hybrid vector approximant related results include the case of a row convergence theorem for a complex valued power series using a clifford inverse instead of the moore penrose inverse

simple analytical approximations to the integrals of the bessel functions jν application to the transmittance of a circular aperture two accurate yet simple analytic approximations to the integral of the bessel function j0 are presented these first and second order approximations are obtained by improving on the recently developed method known as two point quasi rational approximations the accuracy of the first order approximant is better than 0 05 the second order approximant is practically indistinguishable from the true integral even for very large values of the argument overall accuracy is better than 0 002 05 our approximants are in addition analytic and therefore replace with significant advantages both the well known power series and the asymptotic formulae of the integral approximants to the transmittance function of a plane wave through a circular aperture are derived a problem which arises in diffraction theory and particle scattering the second order approximant to the transmittance is analytic too and can be evaluated for small and large values of the argument just with a hand calculator its accuracy is better than 0 0011 as an extension two first order approximations to the integrals of the bessel functions j of fractional order are derived

some exact solutions for the potential r 1 2λr 2λ2r2 the authors show how to obtain an infinite number of exact solutions for the excited states of an s wave hydrogen atom with the polynomial perturbation 2 lambda r 2 lambda 2r2 for certain specific values of lambda the energy eigenvalues in such cases satisfy en 1 2 2n 3 mod lambda mod with the corresponding wavefunctions being given by products of exp mod lambda mod r lambda mod lambda mod r2 and polynomials of nth degree in r

extrapolation methods for vector sequences an analogue of aitken s 2 method suitable for vector sequences is proposed aspects of the numerical performance of the vector algorithm based on using the moore penrose inverse are investigated the fact that the denominator polynomial associated with a vector pade approximant is the square of its equivalent in the scalar case is shown to be a source of approximation error in cases where the convergence of the vector sequence is dominated by real eigenvalues a hybrid form of the vector pade approximant having a denominator polynomial of minimal degree is proposed and its effectiveness is demonstrated on several standard examples

a modified matrix sign function method for projected lyapunov equations abstract in this paper we discuss the numerical solution of projected generalized lyapunov equations using the matrix sign function method such equations arise in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation it is known that the matrix sign function method applied to a matrix pencil e a converges if and only if e a is of index at most 2 the convergence is quadratic if e is nonsingular and it is linear otherwise we will propose a modification of the matrix sign function method that converges quadratically for pencils of arbitrary index numerical examples will be presented to demonstrate the properties of the modified method

determinantal inequalities for diagonally signed matrices and an application to gram cauchy matrices abstract the condition that a hermitian matrix is diagonally signed complementary has recently been shown to guarantee that its signature is invariant with respect to hadamard products with gram matrices in this paper we establish inequalities for the determinants of these diagonally signed matrices that are analogs of well known inequalities for positive definite matrices because hermitian cauchy matrices and their confluent forms are diagonally signed we can then infer from the new inequalities the existence in general of inverses of the confluent forms of hermitian gram cauchy matrices

on modified iterative method for nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions

two point quasifractional approximant in physics method improvement and application to jν x an improved two point quasifractional approximant method is presented that includes a free parameter in the denominator this parameter is determined by minimizing the theoretical truncation error bound thus ensuring high accuracy an added advantage of introducing a free parameter is that defects that are usual in pade approximants are always avoided the method is applied to the fractional bessel functions j x obtaining a unique approximant valid for all positive x that is more accurate than previously published

on the hill determinant method explicit examples are given of the false eigenvalues of the hill determinant method the existence of which has been suspected by workers using analytic methods a simple criterion is discovered for distinguishing between false and physical eigenvalues

alternative theorems for nonlinear projection equations and applications to generalized complementarity problems let k be a closed convex subset in rn and let f g and h be three functions from rn into itself we consider the following nonlinear projection equation npe h x k g x f x x r 1 where k is the orthogonal projection operator onto the set k this equation provides a uni ed formulation of several interesting and important special cases in the case when h x g x for any x rn then 1 reduces to the equation studied by pang and yao 17 under the name of generalized normal equation which is equivalent to the following generalized variational inequality gvi g x k y g x f x 0 for all y k 2

fractional approximations to the bessel function j0 x a method to obtain fractional approximations to the bessel function j0 x is reported here this method improves a recently published one principally in that all the parameters are uniquely determined by linear equations our approximations give fairly good accuracy for all real positive values the maximum absolute error for the first degree approximation is about 0 0035 and for the fourth degree one about 2 8 10 6

introduction to the improved functional epsilon algorithm this paper introduces the improved functional epsilon algorithm we have defined this new method in principle of the modified aitken 2 algorithm moreover we have found that the improved functional epsilon algorithm has remarkable precision of the approximation of the exact solution and there exists a relationship with the integral pade approximant the use of the improved functional epsilon algorithm for accelerating the convergence of sequence of functions is demonstrated the relationship of the improved functional epsilon algorithm with the integral pade approximant is also demonstrated moreover we illustrate the similarity between the integral pade approximant and the modified aitken 2 algorithm thus we have shown that the integral pade approximant is a natural generalisation of modified aitken 2 algorithm

a family of pade type approximants for accelerating the convergence of sequences we describe a collection of pade type methods for accelerating the convergence of sequence of functions the construction and connections of pade s methods with other similar methods are given we examine the effectiveness of these new methods namely integral pade approximant modified pade approximant and squared pade approximant together with the well established methods namely functional pade approximant and classical pade approximant for approximating the characteristic value and corresponding characteristic function estimates of characteristic value and characteristic function derived using integral pade approximants are found to be substantially more accurate than other similar methods

generalized lyapunov equation and factorization of matrix polynomials abstract this paper presents an algorithm for the construction of a solution of the generalized lyapunov equation it is proved that the polynomial matrix factorization relative to the imaginary axis may be reduced to the successive solution of lyapunov equations i e the factorization is reduced to the solution of a sequence of generalized lyapunov equations not to the solution of generalized riccati equation

fractional approximation to elliptic functions the jacobi functions sn x m have been approximated by a quotient of polynomials of first to fourth degrees the method used here is an extension to nonlinear differential equations of one previously published for first and second order linear differential equations that method uses power series and asymptotic expansions simultaneously the accuracy here obtained is very good the absolute error is lower than 10 8 for m 0 8 except for values of the parameter m near 1 they are much better for several orders of magnitude than those based on the pade method for the same number of parameters to be determined

an example of a quantum catastrophe the authors study the excited stage energies of the s wave hydrogen atom with the polynomial perturbation 2 lambda r 2 lambda 2r2 they demonstrate the existence of a discontinuity in the eigenvalue spectrum at lambda 0 as lambda changes from positive to negative

matching of local expansions in the theory of non linear vibrations abstract linear systems are a generalization of normal principal vibrations of linear systems 1 3 in this case all position co ordinates can be defined well from any one of them r m rosenberg is credited with being the first to introduce broad classes of conservative systems allowing normal vibrations with rectilinear trajectories in a configurational space in systems of a more general type trajectories of normal vibrations are curvilinear assume that in a conservative system the potential energy is a positively definite polynomial in the co ordinates at small amplitudes a linear system is to be selected as the initial one while at large amplitudes a homogeneous non linear system allows normal vibrations with rectilinear trajectories in the vicinity of a linear system trajectories of normal vibrations can be determined as power series in the amplitude while in the vicinity of a homogeneous non linear system they can be determined as power series in the inverse amplitude in order to join together local expansions and to investigate the behavior of normal vibration trajectories at arbitrary amplitude values fractional rational diagonal pade approximants are used necessary conditions for the convergence of a succession of pade approximants have been obtained and that allows one to establish relations between quasi linear and essentially non linear expansions that is to decide which of them correspond to the same solution and which to different ones additional modes of vibrations exist only in a non linear systems as the amplitude decreases they vanish at a certain limiting point

approximate proximal algorithms for generalized variational inequalities with paramonotonicity and pseudomonotonicity we propose an approximate proximal algorithm for solving generalized variational inequalities in hilbert space extension to bregman function based approximate proximal algorithm is also discussed weak convergence of these two algorithms are established under the paramonotonicity and pseudomonotonicity assumptions of the operators

fractional approximation to the vacuum vacuum amplitude of a φ4 potential theory in zero dimensions here the vacuum vacuum amplitude with a 4 potential in terms of the fractional approximation to the partition function of a zero dimensional field theory is presented this fractional approximation has been obtained from both the power series and the asymptotic expansion the power series diverges nonetheless the fractional approximations are excellent all the approximations from first to seventh degree are presented with maximum errors from 0 6 to 1 6 10 5 respectively

multiple gain parameter multivariable root locus abstract the multivariable root locus concept is generalized here by allowing for independently variable gain parameters in the different feedback paths sufficient conditions are found under which the matrix of markov parameters of the open loop transfer matrix g s will guarantee stability for every gain matrix in the gain space this generalizes the recent work of byrnes 1981 and cook and hall 1982 and is useful in the design of proportional plus integral controllers for multivariable feedback control systems

spiked and symmetrized decadic potentials supporting elementary n plets of bound states we show that the potential wells v x x10 ax8 bx6 cx4 dx2 f x2 with a central spike possess arbitrary finite multiplets of elementary exact bound states their strong asymptotic growth implies an ambiguity in their symmetrically generalized quantization via complex boundary conditions but the three eligible methods coincide at our exceptional solutions

state feedback decomposition of multivariable systems via block pole placement some recently developed algebraic theorems of matrices and applications to matrix fraction descriptions of a class of multivariable systems are introduced also a new block pole placement is developed for the state feedback block decomposition of multivariable systems

bilevel decision via variational inequalities in this paper we introduce the group decision problems in a bilevel programming structure and its corresponding optimization with equilibrium constraints mpec for short problems for these models we establish new existence results which extend some known results to infinite dimensional space setting we also establish the links between group decision problems in a bilevel programming structure and its corresponding mpec problems in banach spaces an interesting example about the mean variance portfolio optimization is given and the existence and uniqueness results for its corresponding mpec problems are obtained

comments on a paper concerning the analytic continued fraction technique for bound states the author shows that the treatment of bound and confined states for a class of confinement potentials by application of the analytic continued fraction method as presented in a recent paper dalta et al ibid vol 13 p 3161 1980 is erroneous and may lead to wrong results for the eigenvalues of the relevant schrodinger equation

iterative algorithms for a general system of generalized nonlinear mixed composite type equilibria in this paper we consider and study a general system of generalized nonlinear mixed composite type equilibria in hilbert spaces first we prove the existence and uniqueness of the solution for this system of generalized nonlinear mixed composite type equilibria second the mann iterative method with errors is extended to develop some new iterative algorithms for finding approximate solutions for this system of generalized nonlinear mixed composite type equilibria we also derive the strong convergence of the sequences generated by these iterative algorithms in hilbert spaces

the hill determinant an application to a class of confinement potentials it is shown that the method of determination of the eigenvalues in terms of infinite continued fractions for a class of confinement potentials is equivalent to the vanishing of the hill determinant the problem of normalisation of the wavefunction is also discussed

numerical solution and perturbation theory for generalized lyapunov equations we discuss the numerical solution and perturbation theory for the generalized continuoustime lyapunov equation e xa a xe ig with a singular matrix e if this equation has a solution it is not unique we generalize a bartels stewart method and a hammarling method to compute a partial solution of the generalized lyapunov equation with a special right hand side a spectral condition number is introduced and perturbation bounds for such an equation are presented numerical examples are given

the linear complementarity problem under asymptotic analysis in this work we study the classical linear complementarity problem lcp by describing the asymptotic behavior of the approximate solutions to its variational inequality formulation thus some properties satisfied by the directions which are limits of the normalized unbounded approximate solutions will be established based on this analysis various equivalent conditions guaranteeing the existence of solutions to lcp are given in particular the sufficient condition of gowda and pang expressed in terms of the solutions to augmented linear complementarity problems is written in a way that is more easily verifiable our approach allows us to deal with garca a matrices semimonotone copositive q pseudomonotone matrices among others in a unified framework furthermore we introduce a larger class of matrices for which many of the results including a sensitivity one due to gowda and pang are still valid in addition some conditions ensuring the boundedness of the solution set are also provided and some estimates for the asymptotic cone of the solution set for different classes of matrices are given as well hence the present approach sheds new light and offers an alternative to view classical results

generalized vector variational inequalities with star pseudomonotone and discontinuous operators abstract it is well known that a vector variational inequality can be a very efficient model for use in studying vector optimization problems by using the ky fan fixed point theorem and the scalarization method we will prove some existence theorems for strong solutions for generalized vector variational inequalities where discontinuous and star pseudomonotone operators are involved our results can be applied to the study of the existence of solutions of vector optimal problems some examples are given and analyzed

existence and algorithms for the bilevel new generalized mixed equilibrium problems in banach spaces abstract in this paper we introduce and analyze the new generalized mixed equilibrium problems ngmep and the bilevel new generalized mixed equilibrium problems bngmep in banach spaces first by using a minimax inequality some new existence theorems of the solution and the behavior of solution set for the ngmep and the bngmep are obtained in both arbitrary banach spaces with the coercive conditions and a reflexive banach space without the coercive conditions next by using auxiliary principle technique some new iterative algorithms for solving the ngmep and the bngmep are suggested and analyzed the strong convergence of the iterative sequences generated by the algorithms are also proved in both arbitrary banach spaces with the coercive conditions and a reflexive banach space without the coercive conditions these results are new and generalize some recent results in this field

on the numerical properties of the schur approach for solving the matrix riccati equation abstract an a posteriori estimate of the relative error in the solution of the algebraic matrix riccati equation found by the schur approach is derived it is shown that in some cases the schur approach is numerically unstable

shifted 1 n expansion and exact solutions for the potential v r z r gr λr2 the authors have found an infinite number of exact solutions for the hydrogenic atom in the external potential v r gr r2 not only for an s wave state but for higher waves as well from supersymmetric considerations the general schrodinger equation has been treated by the shifted 1 n expansion method the eigenvalues obtained from the shifted 1 n expansion are compared with those obtained by bessis et al 1987 and also with the supersymmetric exact values

solution of integral equations using generalised inverse function valued pade approximants i abstract neumann series solutions for the linear integral equation x 1 1 0 1 x y y d y converge for small values of we use generalised inverse function valued pade approximants to accelerate the convergence of the neumann series and to estimate the singular value of these estimates are found to compare very favourably with those from the fredholm determinant method and the pade approximant method

analytical construction of homoclinic orbits of two and three dimensional dynamical systems abstract an approach for the construction of homoclinic orbits of non linear dynamical systems with phase spaces of dimensions equal to two or three is proposed here the non linear schrodinger equation and lorenz system are considered quasi pade approximants are used for this construction potentiality and convergence conditions used earlier in the theory of non linear normal vibration modes make it possible to solve the boundary value problems formulated for the orbits and to evaluate initial amplitude values

vector valued rational interpolants i it is shown explicitly that the samelson inverse may be used to define vector valued thiele type rational interpolants and the equivalence with claessens algorithm is established for the special case of vector valued pade approximants the general form of mccleod s theorem follows as a corollary

the epsilon algorithm and related topics the epsilon algorithm is recommended as the best all purpose acceleration method for slowly converging sequences it exploits the numerical precision of the data to extrapolate the sequence to its limit we explain its connections with pade approximation and continued fractions which underpin its theoretical base then we review the most recent extensions of these principles to treat application of the epsilon algorithm to vector valued sequences and some related topics in this paper we consider the class of methods based on using generalised inverses of vectors and the formulation specifically includes the complex case wherever possible

vector variational like inequalities with generalized bifunctions defined on nonconvex sets abstract in this paper the nonemptiness and compactness of solution sets for stampacchia vector variational like inequalities for short svvlis and minty vector variational like inequalities for short mvvlis with generalized bifunctions defined on nonconvex sets are investigated by introducing the concepts of generalized weak cone pseudomonotonicity and generalized proper cone suboddness moreover some equivalent relations between a solution of svvlis and mvvlis and a generalized weakly efficient solution of vector optimization problems for short vops are established under the assumptions of generalized pseudoconvexity and generalized invexity in the sense of clarke generalized directional derivative these results extend and improve the corresponding results of others

a complementarity problem in mathematical programming in banach space abstract an existence and uniqueness theorem for the nonlinear complementarity problem over arbitrary closed convex cones in a reflexive real banach space is established

two point quasifractional approximant in physics truncation error the quasifractional approximation method is developed in a systematic manner this method uses simultaneously the power series and at a second point the asymptotic expansion the usual form of the approximants is two or more rational fractions in terms of a suitable variable combined with auxiliary nonfractional functions coincidence in the singularities in the region of interest is pursued equal denominators in the rational fractions is required so that the solution of only linear algebraic equations is needed to determine the parameters of the approximant an upper bound is obtained for the truncation error for a certain class of functions which contains most of the functions for which this method has been applied so far it is shown that quasifractional approximants can be derived as a mixed german and latin polynomial problem in the context of hermite pade approximation theory

new approximations to j sub 0 and j sub 1 bessel functions new approximate solutions to the 0th and 1st order bessel functions of the first kind are derived the formulations are based upon using a new integral with no previously known solution the new integral in the limiting case is identical to the 0th order bessel function integral it is solved in closed form and the solution is expressed as a simple even order polynomial with integer coefficients the polynomial coefficients are all of integer value the 1st order bessel function approximation can then be found through a simple derivative comparisons are made between the exact solution classic solutions and the new approximation the new approximation proves to be much more accurate than the classic small argument approximation it is also sufficiently accurate to bridge the gap between the classic large and small argument approximations and has potential applications in allowing one to analytically evaluate integrals containing bessel functions

hydrogenic atoms in the external potential v r gr λr2 exact solutions and ground state eigenvalue bounds using moment methods an infinite number of exact solutions for the ground and excited states of an s wave hydrogenic atom with the perturbation v r gr lambda r2 are constructed subject to special relations between g lambda and the nuclear charge z a powerful method of stieltjes moments is employed to generate rapidly converging upper and lower bounds to the ground state energy e0 z g lambda for arbitrary g z and positive lambda the accuracies of these bounds are relatively insensitive to the strength of the perturbation the moment method also generates the exact s wave ground state solutions mentioned above

matrix sign function methods for solving projected generalized continuous time sylvester equations in this technical note we investigate the numerical solution of the projected generalized sylvester equations via a matrix sign function method such equations arise in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation unlike the classical matrix sign function iteration we propose a modification of the matrix sign function method that converges quadratically for pencils of arbitrary index numerical experiments report the effectiveness of the modified method

confluent hermitian cauchy matrices are diagonally signed abstract it is shown that cauchy matrices admit a confluent extension in much the same way that confluent vandermonde matrices or cauchy alternants have confluent forms cauchy matrices formed from distinct elements have been proved recently to be diagonally signed and this is equivalent to showing that they are complementary matrices we show here that this property extends to the confluent case too

discrete generalized algebraic riccati equations and polynomial matrix factorization abstract this paper presents an algorithm for solving discrete generalized algebraic riccati equations with the help of an orthogonal projector a generalization of the procedure of forming and correcting the orthogonal projector is considered and also that of correcting the proper solution by the newton raphson scheme the possibility to use the discrete generalized riccati equations for polynomial matrix factorization with respect to the unit circle is demonstrated a numerical example is given

existence results for the nonlinear complementarity problem and applications to nonlinear analysis abstract we produce an existence result for the nonlinear complementarity problem associated to a weakly locally compact convex cone k in a banach space e and to the difference j f of two nonlinear operators we specialize our result to the case where k is a so called galerkin cone j is the duality mapping and f satisfies a suitable growth condition applications to the fixed point theory and to eigenvalue problems conclude the paper

fractional approximations for the spherically symmetric coulomb scattering wave functions an improved method is presented for obtaining fractional approximations the fractional parameters are now solutions of a set of linear equations and no nonlinear equations are involved as in the previous procedure excellent fractional approximations are presented for the coulomb functions for 0 5 1 2 and 5 the accuracy is sufficient for most of the computations where this function is used the straightforward extension to higher orders is indicated

false eigenvalues of the hill determinant method it is shown analytically that the false eigenenergies of a potential obtained by the method of hill determinants are the physical energies of a different potential

a new hybrid iterative algorithm for variational inequalities let h be a real hilbert space let f h h be a strongly monotone and lipschitzian mapping let t n n 1 h h be an infinite family of non expansive mappings with common fixed points set n 1 fix t n a we devise an iterative algorithmy n x email protected nf x n x n 1 email protected n y email protected nw ny n n 0 where l n is a sequence in 0 a n is a sequence in 0 1 and w n is the w mapping we prove that the sequence x n converges in norm to x email protected n 1 fix t n which is the unique solution of the following variational inequality 0 email protected email protected n 1 fix t n

on general systems of variational inequalities in this paper we present a new relaxed viscosity approximation method and prove the strong convergence of the method to a common fixed point of finitely many nonexpansive mappings and a strict pseudocontraction that also solves a suitable equilibrium problem and a general system of variational inequalities