nested splitting conjugate gradient method for matrix equation axb c and preconditioning in this paper we present a nested splitting conjugate gradient nscg iteration method for solving a class of matrix equations with nonsymmetric coefficient matrices this method is actually inner outer iterations which employs a cg like method as inner iteration to approximate each outer iterate while each outer iteration is induced by a convergent and symmetric positive definite splitting of the coefficient matrices convergence conditions of this method are studied in depth and numerical experiments show the efficiency of this method moreover we show that the use of the quasi hermitian splitting as a preconditioner can induce an accurate robust and effective preconditioned krylov subspace method

an iterative method for the skew symmetric solution and the optimal approximate solution of the matrix equation axb c in this paper an iterative method is constructed to solve the linear matrix equation axb c over skew symmetric matrix x by the iterative method the solvability of the equation axb c over skew symmetric matrix can be determined automatically when the equation axb c is consistent over skew symmetric matrix x for any skew symmetric initial iterative matrix x 1 the skew symmetric solution can be obtained within finite iterative steps in the absence of roundoff errors the unique least norm skew symmetric iterative solution of axb c can be derived when an appropriate initial iterative matrix is chosen a sufficient and necessary condition for whether the equation axb c is inconsistent is given furthermore the optimal approximate solution of axb c for a given matrix x 0 can be derived by finding the least norm skew symmetric solution of a new corresponding matrix equation email protected email protected finally several numerical examples are given to illustrate that our iterative method is effective

on the global krylov subspace methods for solving general coupled matrix equations in the present paper we propose the global full orthogonalization method gl fom and global generalized minimum residual gl gmres method for solving large and sparse general coupled matrix equations j 1pa i jx jb i j c i i 1 p where a i j r m x m b i j r n x n c i r m x n i j 1 2 p are given matrices and x i r m x n i 1 2 p are the unknown matrices to do so first a new inner product and its corresponding matrix norm are defined then using a linear operator equation and new matrix product we demonstrate how to employ gl fom and gl gmres algorithms for solving general coupled matrix equations finally some numerical experiments are given to illustrate the validity and applicability of the results obtained in this work

nonlinear three point third order boundary value problems abstract in this paper we consider three point boundary value problems for third order differential equations we provide simple sufficient conditions in order to obtain a priori bounds on solutions we then rely on the topological transversality theorem of granas or on schaefer s theorem to prove existence of solutions

gradient based iterative algorithm for solving coupled matrix equations abstract this paper is concerned with iterative methods for solving a class of coupled matrix equations including the well known coupled markovian jump lyapunov matrix equations as special cases the proposed method is developed from an optimization point of view and contains the well known jacobi iteration gauss seidel iteration and some recently reported iterative algorithms by using the hierarchical identification principle as special cases we have provided analytically the necessary and sufficient condition for the convergence of the proposed iterative algorithm simultaneously the optimal step size such that the convergence rate of the algorithm is maximized is also established in explicit form the proposed approach requires less computation and is numerically reliable as only matrix manipulation is required some other existing results require either matrix inversion or special matrix products numerical examples show the effectiveness of the proposed algorithm

third order differential equations with integral boundary conditions abstract in this paper we study nonlinear third order differential equations with integral boundary conditions we provide sufficient conditions on the nonlinearity and the functions appearing in the boundary conditions that guarantee the existence of at least one solution to our problem our technique is based on a priori bounds and fixed point theorems

a modified gradient based algorithm for solving sylvester equations abstract in this paper a modified gradient based algorithm for solving sylvester equations is presented different from the gradient based method introduced by ding and chen 7 and the relaxed gradient based algorithm proposed by niu et al 18 the information generated in the first half iterative step is fully exploited and used to construct the approximate solution theoretical analysis shows that the new method converges under certain assumptions numerical results are given to verify the efficiency of the new method

new convergence results on the global gmres method for diagonalizable matrices in the present paper we give some new convergence results of the global gmres method for multiple linear systems in the case where the coefficient matrix a is diagonalizable we derive new upper bounds for the frobenius norm of the residual we also consider the case of normal matrices and we propose new expressions for the norm of the residual

consistency for bi skew symmetric solutions to systems of generalized sylvester equations over a finite central algebra let be a finite dimensional central algebra with an involutorial antiautomorphism and char 2 n n be the set of all n n matrices over a aij n n is called bisymmetric if aij an i 1 n j 1 aji and biskewsymmetric if aij an i 1 n j 1 aji the following systems of generalized sylvester equations over a1x yb1 c1 i asx ybs cs a1xb1 c1xd1 e1 ii asxbs csxds es are considered necessary and sufficient conditions are given for the existence of constant solutions with bi skew symmetric constrains to i and ii as a particular case auxiliary results dealing with the system of sylvester equations are also presented

iterative algorithms for solving the matrix equation axb cx td e in this paper we propose two iterative algorithms to solve the matrix equation axb cx td e the first algorithm is applied when the matrix equation is consistent in this case for any special initial matrix x 1 a solution the minimal frobenius norm solution can be obtained within finite iteration steps in the absence of roundoff errors the second algorithm is applied when the matrix equation is inconsistent in this case for any special initial matrix x 1 a least squares solution the minimal frobenius norm least squares solution can be obtained within finite iteration steps in the absence of roundoff errors some examples verify the efficiency of these algorithms

solving linearly constrained matrix least squares problem by lsqr abstract matrix iterative algorithm lsqr is proposed for solving the linearly constrained matrix least squares ls problem with the special properties of constraint matrix kronecker product and the coordinate mapping from the constrained space to its independent parameter space we transform the constrained matrix ls problem to the unconstrained long vector least squares problem and rewrite the corresponding vector form algorithm back to the matrix one the resulting matrix form iteration only consists of matrix matrix product and does not involve the kronecker product numerical results are reported to show the feasibility of the proposed method

gradient based iterative solutions for general linear matrix equations in this paper we present a gradient based iterative algorithm for solving general linear matrix equations by extending the jacobi iteration and by applying the hierarchical identification principle convergence analysis indicates that the iterative solutions always converge fast to the exact solutions for any initial values and small condition numbers of the associated matrices two numerical examples are provided to show that the proposed algorithm is effective

fully dynamic point location in a monotone subdivision in this paper a dynamic technique for locating a point in a monotone planar subdivision whose current number of vertices is n is presented the complete set of update operations are insertion o

singular value and generalized singular value decompositions and the solution of linear matrix equations abstract the solution of the linear matrix equations i axb cyd e and ii axb fxg e h are considered new necessary and sufficient conditions for the consistency of the equations are derived some using the generalized singular value decomposition special cases iii ax yd e and iv axb e are treated using the singular value decomposition numerical algorithms for the solutions are also suggested

iterative solutions of the generalized sylvester matrix equations by using the hierarchical identification principle abstract in this paper by extending the well known jacobi and gauss seidel iterations for ax b we study iterative solutions of matrix equations axb f and generalized sylvester matrix equations axb cxd f including the sylvester equation ax xb f as a special case and present a gradient based and a least squares based iterative algorithms for the solution it is proved that the iterative solution always converges to the exact solution for any initial values the basic idea is to regard the unknown matrix x to be solved as the parameters of a system to be identified and to obtain the iterative solutions by applying the hierarchical identification principle finally we test the algorithms and show their effectiveness using a numerical example

an iterative method for the least squares symmetric solution of the linear matrix equation axb c abstract this paper an iterative method is presented to solve the minimum frobenius norm residual problem min axb c with unknown symmetric matrix x by this iterative method for any initial symmetric matrix x0 a solution x can be obtained within finite iteration steps in the absence of roundoff errors and the solution x with least norm can be obtained by choosing a special kind of initial symmetric matrix in addition the unique optimal approximation solution x to a given matrix x in frobenius norm can be obtained by first finding the least norm solution x of the new minimum residual problem min a x b c with unknown symmetric matrix x where c c a x x t 2 b given numerical examples are show that the iterative method is quite efficient

the general coupled matrix equations over generalized bisymmetric matrices abstract in the present paper by extending the idea of conjugate gradient cg method we construct an iterative method to solve the general coupled matrix equations j 1 p a ij x j b ij m i i 1 2 p including the generalized coupled lyapunov and sylvester matrix equations as special cases over generalized bisymmetric matrix group x 1 x 2 x p by using the iterative method the solvability of the general coupled matrix equations over generalized bisymmetric matrix group can be determined in the absence of roundoff errors when the general coupled matrix equations are consistent over generalized bisymmetric matrices a generalized bisymmetric solution group can be obtained within finite iteration steps in the absence of roundoff errors the least frobenius norm generalized bisymmetric solution group of the general coupled matrix equations can be derived when an appropriate initial iterative matrix group is chosen in addition the optimal approximation generalized bisymmetric solution group to a given matrix group x 1 x 2 x p in frobenius norm can be obtained by finding the least frobenius norm generalized bisymmetric solution group of new general coupled matrix equations the numerical results indicate that the iterative method works quite well in practice

bcr method for solving generalized coupled sylvester equations over centrosymmetric or anti centrosymmetric matrix abstract this paper introduces another version of biconjugate residual method bcr for solving the generalized coupled sylvester matrix equations over centrosymmetric or anti centrosymmetric matrix we prove this version of bcr algorithm can find the centrosymmetric solution group of the generalized coupled matrix equations for any initial matrix group within finite steps in the absence of round off errors furthermore a method is provided for choosing the initial matrices to obtain the least norm solution of the problem at last some numerical examples are provided to illustrate the efficiency and validity of methods we have proposed

on iterative solutions of general coupled matrix equations in this paper we study coupled matrix equations which are encountered in many systems and control applications first we extend the well known jacobi and gauss seidel iterations and present a large family of iterative methods which are then applied to develop iterative solutions to coupled sylvester matrix equations the basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified and to obtain the iterative solutions by applying a hierarchical identification principle next we generalize the sylvester equations to general coupled matrix equations and propose a gradient based iterative algorithm for the solutions using a block matrix inner product the star star product we prove that the iterative algorithm always converges to the unique solutions for any initial values one advantage of the algorithms proposed is that they require less storage space in implementation than existing numerical methods finally we test the algorithms and show their effectiveness using numerical examples

an iterative algorithm for the least frobenius norm least squares solution of a class of generalized coupled sylvester transpose linear matrix equations abstract the iterative algorithm of a class of generalized coupled sylvester transpose matrix equations is presented we prove that if the system is consistent a solution can be obtained within finite iterative steps in the absence of round off errors for any initial matrices if the system is inconsistent the least squares solution can be obtained within finite iterative steps in the absence of round off errors furthermore we provide a method for choosing the initial matrices to obtain the least frobenius norm least squares solution of the problem finally numerical examples are presented to demonstrate that the algorithm is efficient

time domain galerkin method for dynamic load identification summary this paper proposes a new method called time domain galerkin method tdgm for investigating the structural dynamic load identification problems firstly the shape functions are adopted to approximate three parameters such as the dynamic load kernel function response and measured structural response secondly defining a residual function could be expressed as the difference of the measured response and the computational response thirdly select an appropriate weighting function to multiply the defined residual function and make integral operation with respect to time to be zero finally when the shape functions are chosen as the weighting function it establishes the forward model called tdgm furthermore the regularization method could have effectiveness in solving the ill posed matrix of load reconstruction and obtaining the accurate identified results of the dynamic load compared with the traditional green kernel function method gkfm tdgm can effectively overcome the influences of noise and improve the accuracy of the dynamic load identification three numerical examples are provided to demonstrate the correctness and advantages of tdgm copyright 2015 john wiley sons ltd

implicitly restarted global fom and gmres for nonsymmetric matrix equations and sylvester equations the global gmres and global fom algorithm are recently proposed by jbilou et al for solving the linear equations with multiple right hand sides k jbilou a messaoudi h sados global fom and gmres algorithms for matrix equations appl numer math 31 1999 49 63 like gmres for the linear equations they generally uses restarting which slows the convergence however some information can be retained at the time of the restart and used in the next cycle we present algorithms that use implicit restarting in order to retain this information as morgan have proposed recently r b morgan implicitly restarted gmres and arnoldi methods for nonsymmetric systems of equations siam j matrix anal appl 21 2000 1112 1135 at the same time we prove that global gmres and global fom methods for matrix equations are equivalent with the corresponding methods for linear equations and propose implicitly restarted global fom and gmres numerical examples show that our methods are efficient

existence result for impulsive third order periodic boundary value problems this paper is devoted to the study of periodic boundary value problems for nonlinear third order differential equations subjected to impulsive effects we provide sufficient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one periodic solution our approach is based on a priori estimates the method of upper and lower solutions combined with an iterative technique which need not be monotone

dynamic reachability in planar digraphs with one source and one sink abstract in this paper we investigate the reachability problem on spherical st graphs which are planar acyclic digraphs with exactly one source and exactly one sink these digraphs find specific applications to visibility representations planarity testing planar graph embedding graph drawing and motion planning let n be the number of vertices first we show that reachability queries in a spherical st graph can be answered in o 1 time using an o n space data structure that can be constructed in o n time next we present a dynamic data structure which uses o n space and supports reachability queries and updates in o log n time finally we show how to extend these results to planar digraphs that have one source and one sink and may have directed cycles

on three point boundary value problems associated with third order differential equations introduction in this paper we shall be concerned with the existence and uniqueness of solutions to three point boundary value problems associated with the differential equation y f x y y s y 1 1 where f x y z w is assumed to be continuous on a subset of r4 initial value problems associated with 1 1 exist and are unique in the interval x1 x a monotonicity restriction on f x y z w ensures that the following boundary value problems y j x y y y y xj y y xj y y x m i 1 2 12i y j x y y y y x y y x m2 2 2 9 y x y i 421 le3i

a note on the numerical approximate solutions for generalized sylvester matrix equations with applications abstract in the present paper we propose a krylov subspace method for solving large and sparse generalized sylvester matrix equations the proposed method is an iterative projection method onto matrix krylov subspaces as a particular case we show how to adapt the ilu and the ssor preconditioners for solving large sylvester matrix equations numerical examples and applications to some pde s will be given

a shifted complex global lanczos method and the quasi minimal residual variant for the stein conjugate matrix equation x ax b c abstract in this paper based on a complex global lanczos process a shifted complex global lanczos method is proposed to solve the stein conjugate matrix equation x a x b c the new method adopts the shifted technique and is implemented by the original coefficient matrices the direct version of the proposed method is derived by exploiting the special structure of the l u factorization moreover the quasi minimal residual variant is developed to stabilize the convergence behavior finally some numerical examples are given to illustrate the effectiveness with comparison to some existing methods

amortized efficiency of a path retrieval data structure a data structure is presented for the problem of maintaining a digraph under an arbitrary sequence of two kinds of operations an add operation that inserts an arc in the digraph and a searchpath operation that checks the presence of a path between a pair of nodes our data structure supports both operations in o n amortized time and requires o n2 space where n is the number of nodes in the digraph

existence of triple positive solutions for a third order three point boundary value problem in this paper we investigate the existence of triple positive solutions for the nonlinear third order three point boundary value problem u t a t f t u t u t u t 0 0 q 0 1 0 are continuous first green s function for the associated linear boundary value problem is constructed and then by using a fixed point theorem due to avery and peterson we establish results on the existence of triple positive solutions to the boundary value problem

existence of solutions for a class of third order nonlinear boundary value problems abstract in this paper we are concerned with the following third order ordinary differential equation x t f t x t x t x t 0 0 with the nonlinear boundary conditions x 0 0 g x 0 x 0 a h x 1 x 1 b where a b r f 0 1 r 3 r is continuous g h r 2 r are continuous the existence result is given by using a priori estimate nagumo condition upper and lower solutions and leray schauder degree and we give an example to demonstrate our result

the symmetric solution of the matrix equations ax ya c axat bybt c and atxa btxb c d abstract the necessary and sufficient conditions for the existence of and the expressions for the symmetric solutions of matrix equations i ax ya c ii axa t byb t c and iii a t xa b t xb c d are derived in addition the minimum 2 norm least squares symmetric solution of equation i the minimum 2 norm symmetric solution of equation ii and the least squares solution of equation iii are obtained

compact oracles for reachability and approximate distances in planar digraphs it is shown that a planar digraph can be preprocessed in near linear time producing a near linear space oracle that can answer reachability queries in constant time the oracle can be distributed as an o log n space label for each vertex and then we can determine if one vertex can reach another considering their two labels only the approach generalizes to give a near linear space approximate distances oracle for a weighted planar digraph with weights drawn from 0 n it approximates distances within a factor 1 e in o log log nn 1 e time our scheme can be extended to find and route along correspondingly short dipaths

a note on the iterative solutions of general coupled matrix equation abstract recently ding and chen f ding t chen on iterative solutions of general coupled matrix equations siam j control optim 44 2006 2269 2284 developed a gradient based iterative method for solving a class of coupled sylvester matrix equations the basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified so that the iterative solutions are obtained by applying hierarchical identification principle in this note by considering the coupled sylvester matrix equation as a linear operator equation we give a natural way to derive this algorithm we also propose some faster algorithms and present some numerical results

convergence properties of some block krylov subspace methods for multiple linear systems in the present paper we give some convergence results of the global minimal residual methods and the global orthogonal residual methods for multiple linear systems using the schur complement formulae and a new matrix product we give expressions of the approximate solutions and the corresponding residuals we also derive some useful relations between the norm of the residuals

on solutions of matrix equation axb cyd f in this paper the matrix equation with two unknown matrices x y of form axb cyd f is discussed by applying the canonical correlation decomposition ccd of matrix pairs we obtain expressions of the least squares solutions of the matrix equation and sufficient and necessary conditions for the existence and uniqueness of the solutions we also derive a general form of the solutions we also study the least squares hermitian skew hermitian solutions of equation axah cych f

new approaches for solving large sylvester equations in this paper we propose two new algorithms based on modified global arnoldi algorithm for solving large sylvester matrix equations ax xb c where a r n x n b r s x s x and c r n x s these algorithms are based on the global fom and gmres algorithms and we call them by global fom sylvester like gfsl and global gmres sylvester like ggsl algorithms respectively some theoretical results and numerical examples are also given

matrix iterative solutions to the least squares problem of bxat f with some linear constraints abstract matrix iterative algorithms are proposed for solving the matrix least square problem of bxat f with variant linear constraints on solutions such as symmetry skew symmetry and symmetry skew symmetry commuting with a given symmetric matrix p we characterize the linear mapping from the constrained solution sets to their independent parameter spaces and use these properties to deduce the matrix iterations based on the classical algorithm lsqr for solving unconstrained ls problem numerical results are reported that show the efficiency of the proposed methods

global fom and gmres algorithms for a class of complex matrix equations abstract in this paper a generalized global arnoldi process is given to produce an f orthonormal basis of complex matrix space then we propose the global full orthogonalization method gl fom and global generalized minimum residual gl gmres method for solving a class of complex matrix equations the new methods can be implemented by the original coefficient matrices by using schur complement we give the expressions of the approximate solutions and the corresponding residuals some convergence results of the proposed methods are also derived finally numerical examples are given to illustrate the effectiveness with comparison to other existing methods

an efficient data structure for lattice operations in this paper we consider the representation and management of an element set on which a lattice partial order relation is defined in particular let n be the element set size we present an nradn space implicit data structure for performing the following set of basic operations 1 test the presence of an order relation between two given elements in constant time 2 find a path between two elements whenever one exists in o l steps where l is the path length 3 compute the successors and or predecessors set of a given element in o h steps where h is the size of the returned set 4 given two elements find all elements between them in time o k log d where k is the size of the returned set and d is the maximum in degree or out degree in the transitive reduction of the order relation 5 given two elements find the least common ancestor and or the greatest common successor in o sqrt n time 6 given k elements find the least common ancestor and or the greatest common successor in o sqrt n k log n time unless stated otherwise all logarithms are to the base 2 the preprocessing time is o n2 focusing on the first operation representing the building box for all the others we derive an overall nradn space times time bound which beats the order n2 bottleneck representing the present complexity for this problem moreover we will show that the complexity bounds for the first three operations are optimal with respect to the worst case additionally a stronger result can be derived in particular it is possible to represent a lattice in space o n sqrt t where t is the minimum number of disjoint chains which partition the element set

krylov subspace methods for the generalized sylvester equation abstract in the paper we propose galerkin and minimal residual methods for iteratively solving generalized sylvester equations of the form axb x c the algorithms use krylov subspace for which orthogonal basis are generated by the arnoldi process and reduce the storage space required by using the structure of the matrix we give some convergence results and present numerical experiments for large problems to show that our methods are efficient

cg type algorithms to solve symmetric matrix equations the global fom and gmres are among the effective algorithms to solve linear system of equations with multiple right hand sides in this paper we study these algorithms in the case that the coefficient matrix is symmetric and extract two cg type algorithms for solving symmetric linear systems of equations with multiple right hand sides then we compare the numerical performance of the new algorithms with some available methods numerical experiments are done on some test matrices from harwell boeing collection

restarted global fom and gmres algorithms for the stein like matrix equation x m x c abstract in this paper we propose the restarted global full orthogonalization method gl fom and global generalized minimum residual gl gmres method to solve the stein like matrix equation x m x c with m x a x b m x a x b m x a x b or m x a x h b respectively where x is an unknown matrix to be solved first by using a real inner product in complex matrix spaces a generalized global arnoldi process is given then we demonstrate how to employ the restarted gl fom and gl gmres algorithms for solving the stein like matrix equation the proposed algorithms take advantage of the shifted structure of the matrix equation and are implemented by the original coefficient matrices finally some numerical examples are given to illustrate the effectiveness with comparison to some existing methods

existence of solution for discontinuous third order boundary value problems abstract in this paper we obtain existence results for the problem u q u f t u with boundary conditions u a a u b b u a c and u a u b u a u b u a c we assume f a caratheodory function q l r 0 such that 1 q l loc r 0 and suppose the existence of lower and upper solutions the existence of solution for the first considered conditions is obtained as a consequence of the fixed points theorems we obtain the solution of the second problem as a limit of solutions of the first case for the first problem the monotone method is developed

projection methods for large lyapunov matrix equations abstract in the present paper we propose krylov subspace methods for solving large lyapunov matrix equations of the form ax xat bbt 0 where a and b are real n n and n s matrices respectively with s n such problems appear in many areas of control theory such as the computation of hankel singular values model reduction algorithms and others the proposed methods are based on the arnoldi process we show how to extract low rank approximate solutions to lyapunov matrix equations and give some theoretical results finally some numerical tests will be reported to illustrate the effectiveness of the proposed method

iterative method to solve the generalized coupled sylvester transpose linear matrix equations over reflexive or anti reflexive matrix abstract the iterative method of generalized coupled sylvester transpose linear matrix equations a x b c y t d s 1 e x t f g y h s 2 over reflexive or anti reflexive matrix pair x y is presented on the condition that the coupled matrix equations are consistent we show that the solution pair x y proposed by the iterative method can be obtained within finite iterative steps in the absence of roundoff error for any initial value given a reflexive or anti reflexive matrix moreover the optimal approximation reflexive or anti reflexive matrix solution pair to an arbitrary given reflexive or anti reflexive matrix pair can be derived by searching the least frobenius norm solution pair of the new generalized coupled sylvester transpose linear matrix equations finally some numerical examples are given which illustrate that the introduced iterative algorithm is quite efficient

the modified conjugate gradient methods for solving a class of generalized coupled sylvester transpose matrix equations in this paper we consider the iteration solutions of generalized coupled sylvester transpose matrix equations a1xb1 c1ytd1 f1 a2yb2 c2xtd2 f2 when the coupled matrix equations are consistent we propose a modified conjugate gradient method to solve the equations and prove that a solution x y can be obtained within finite iterative steps in the absence of roundoff error for any initial value furthermore we show that the minimum norm solution can be got by choosing a special kind of initial matrices when the coupled matrix equations are inconsistent we present another modified conjugate gradient method to find the least squares solution with the minimum norm finally some numerical examples are given to show the behavior of the considered algorithms

weighted least squares solutions to general coupled sylvester matrix equations this paper is concerned with weighted least squares solutions to general coupled sylvester matrix equations gradient based iterative algorithms are proposed to solve this problem this type of iterative algorithm includes a wide class of iterative algorithms and two special cases of them are studied in detail in this paper necessary and sufficient conditions guaranteeing the convergence of the proposed algorithms are presented sufficient conditions that are easy to compute are also given the optimal step sizes such that the convergence rates of the algorithms which are properly defined in this paper are maximized and established several special cases of the weighted least squares problem such as a least squares solution to the coupled sylvester matrix equations problem solutions to the general coupled sylvester matrix equations problem and a weighted least squares solution to the linear matrix equation problem are simultaneously solved several numerical examples are given to illustrate the effectiveness of the proposed algorithms

a new modification of the adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations abstract in this paper we propose a new modified recursion scheme for the resolution of multi order and multi point boundary value problems for nonlinear ordinary and partial differential equations by the adomian decomposition method adm our new approach including duan s convergence parameter provides a significant computational advantage by allowing for the acceleration of convergence and expansion of the interval of convergence during calculations of the solution components for nonlinear boundary value problems in particular for such cases when one of the boundary points lies outside the interval of convergence of the usual decomposition series we utilize the boundary conditions to derive an integral equation before establishing the recursion scheme for the solution components thus we can derive a modified recursion scheme without any undetermined coefficients when computing successive solution components whereas several prior recursion schemes have done so this modification also avoids solving a sequence of nonlinear algebraic equations for the undetermined coefficients fraught with multiple roots which is required to complete calculation of the solution by several prior modified recursion schemes using the adm

a data structure for lattice representation in this paper we present an implicit data structure for the representation of a partial lattice l s n which allows to test the partial order relation among two given elements in constant time the data structure proposed has an overall o n n space complexity where n is the size of ground set n which we will prove to be optimal in the worst case hence we derive an overall o n n space time bound for the relation testing problem thus beating the o n2 bottle neck representing the present complexity the overall pre processing time is o n2

an efficient algorithm for the least squares reflexive solution of the matrix equation a1xb1 c1 a2xb2 c2 abstract a n n real matrix p is said to be a real generalized reflection matrix if pt p and p2 i a n n real matrix x is said to be a reflexive matrix with respect to the generalized reflection matrix p if x pxp in this paper the concept of gradient matrix f x is presented and an algorithm is constructed to solve the reflexive with respect to the generalized reflection matrix p solution of the minimum frobenius norm residual problem a 1 xb 1 a 2 xb 2 c 1 c 2 min by this algorithm for any initial reflexive matrix x1 a solution x can be obtained within finite iteration steps in the absence of roundoff errors and the solution x with least norm can be obtained by choosing a special kind of initial reflexive matrix in addition in the solution set of above problem the unique optimal approximation solution x to a given matrix x0 in frobenius norm can be obtained by finding the least norm reflexive solution x of the new minimum residual problem min a 1 x b 1 a 2 x b 2 c 1 c 2 where c 1 c 1 a 1 x 0 b 1 c 2 c 2 a 2 x 0 b 2 given numerical examples show that the iterative method is quite efficient

efficient point location in a convex spatial cell complex in this paper we propose a new approach to point location in a three dimensional cell complex em p which may be viewed as a nontrivial generalization of a corresponding two dimensional technique due to sarnak and tarjan specifically in a space sweep of em p the intersections of the sweep plane with em p occurring in a slab i e between two consecutive vertices are topologically conformal planar subdivisions if we view the sweep direction as time the descriptions of the various slabs are distinct versions of a two dimensional point location data structure dynamically updated each time we sweep a vertex combining the persistence addition techniques of driscoll em et al with our recently discovered dynamic structure for planar point location in monotone subdivisions we obtain a method with query time o log 2 n and space o n log 2 n for point location in a convex cell complex with em n facets

sufficient conditions for the convergent splittings of non hermitian positive definite matrices abstract we present sufficient conditions for the convergent splitting of a non hermitian positive definite matrix these results are applicable to identify the convergence of iterative methods for solving large sparse system of linear equations

global least squares method gl lsqr for solving general linear systems with several right hand sides abstract in this paper we propose a new method for solving general linear systems with several right hand sides this method is based on global least squares method and reduces the original matrix to the lower bidiagonal form we derive a simple recurrence formula for generating the sequence of approximate solutions x k some theoretical properties of the new method are discussed and we also show that how this method can be implemented for the sylvester equation finally some numerical experiments on test matrices are presented to show the efficiency of the new method

on the generalized sylvester mapping and matrix equations general parametric solution to a family of generalized sylvester matrix equations arising in linear system theory is presented by using the so called generalized sylvester mapping which has some elegant properties the solution consists of some polynomial matrices satisfying certain conditions and a parametric matrix representing the degree of freedom in the solution the results provide great convenience to the computation and analysis of the solutions to this family of equations and can perform important functions in many analysis and design problems in linear system theory it is also expected that this so called generalized sylvester mapping tool may have some other applications in control system theory

on the least squares generalized hamiltonian solution of generalized coupled sylvester conjugate matrix equations abstract in this paper we discuss the finite iterative algorithm to solve a class of generalized coupled sylvester conjugate matrix equations we prove that if the system is consistent an exact generalized hamiltonian solution can be obtained within finite iterative steps in the absence of round off errors for any initial matrices if the system is inconsistent the least squares generalized hamiltonian solution can be obtained within finite iterative steps in the absence of round off errors furthermore we provide a method for choosing the initial matrices to obtain the minimum norm least squares generalized hamiltonian solution of the system finally numerical examples are presented to demonstrate the algorithm is efficient