equivariant quantizations of symmetric algebras abstract let g be a lie bialgebra and let v be a finite dimensional g module we study deformations of the symmetric algebra of v which are equivariant with respect to an action of the quantized enveloping algebra u h g resp u q g we investigate in particular such quantizations obtained from the quantization of certain lie bialgebra structures on the semidirect product of g and v we classify these structure in the important special case when g is complex simple with quasitriangular lie bialgebra structure and v is a simple g module we then introduce a more general notion co poisson module algebras and their quantizations to further address the problem and show that many known examples of quantized symmetric algebras can be described in this language

irreducibility and extensions of ostrowski s theorem abstract in this paper an extension of ostrowski s theorem for complex square irreducible matrices is presented also extensions of similar statements for square complex matrices are analyzed and completed most of the statements in this work cover also the case of reducible matrices

convergent difference schemes for degenerate elliptic and parabolic equations hamilton jacobi equations and free boundary problems convergent numerical schemes for degenerate elliptic partial differential equations are constructed and implemented simple conditions are identified which ensure that nonlinear finite difference schemes are monotone and nonexpansive in the maximum norm explicit schemes endowed with an explicit cfl condition are built for time dependent equations and are used to solve stationary equations iteratively explicit and implicit formulations of monotonicity for first and second order equations are unified bounds on orders of accuracy are established an example of a scheme which is stable but nonmonotone and nonconvergent is presented schemes for hamilton jacobi equations obstacle problems one phase free boundary problems and stochastic games are built and computational results are presented

braided symmetric algebras of simple uq sl2 modules and their geometry in the present paper we prove decomposition formulae for the braided symmetric powers of simple uq sl2 modules natural quantum analogues of the classical symmetric powers of a module over a complex semisimple lie algebra we show that their point modules form natural non commutative curves and surfaces and conjecture that braided symmetric algebras give rise to an interesting non commutative geometry which can be viewed as a flat deformation of the geometry associated to their classical limits

some convergence results for howard s algorithm this paper deals with convergence results of howard s algorithm for the resolution of min a in mathcal a b a x c a 0 where b a is a matrix c a is a vector and mathcal a is a compact set we show a global superlinear convergence result under a monotonicity assumption on the matrices b a extensions of howard s algorithm for a max min problem of the form max b in mathcal b min a in mathcal a b a b x c a b 0 are also proposed in the particular case of an obstacle problem of the form min ax b x g 0 where a is an n times n matrix satisfying a monotonicity assumption we show the convergence of howard s algorithm in no more than n iterations instead of the usual 2 n bound still in the case of an obstacle problem we establish the equivalence between howard s algorithm and a primal dual active set algorithm m hintermuller k ito and k kunisch siam j optim 13 2002 pp 865 888 the algorithms are illustrated on the discretization of nonlinear pdes arising in the context of mathematical finance american option and merton s portfolio problem of front propagation problems and for the double obstacle problem

infinity norm bounds for the inverse of nekrasov matrices using scaling matrices abstract for many applications it is convenient to have good upper bounds for the norm of the inverse of a given matrix in this paper we obtain such bounds when a is a nekrasov matrix by means of a scaling matrix transforming a into a strictly diagonally dominant matrix numerical examples and comparisons with other bounds are included the scaling matrices are also used to derive new error bounds for the linear complementarity problems when the involved matrix is a nekrasov matrix these error bounds can improve considerably other previous bounds

an iterative criterion for h matrices we provide an algorithmic characterization of h matrices when a is an h matrix this algorithm determines a positive diagonal matrix d such that ad is strictly row diagonally dominant in effect d is produced iteratively by quantifying and

an extended compact profile iterative method criterion for sparse h matrices in the theory and applications of numerical linear algebra the class of h matrices is very important for example when one is interested in the solution of linear systems of algebraic equations and their solution is sought by classical iterative methods e g jacobi gauss seidel sor ssor etc in recent years many works have appeared that propose criteria for a

a finite time horizon optimal stopping problem with regime switching we extend the technique developed in e bayraktar a proof of the smoothness of the finite time horizon american put option for jump diffusion http arxiv org abs math 0703782 2007 to a class of finite time horizonal optimal stopping problems under regime switching models which includes the pricing of american put options the construction involved also leads to a computational procedure for the solutions of such optimal stopping problems

on iterative criteria for h and non h matrices the identification of the h matrix property of the coefficient matrix of a linear system of equations is of great theoretical and practical importance since h matrices have many applications in science and engineering for this identification many direct and iterative criteria already exist in this article we present new iterative criteria which are proved to be faster than similar previous ones for the desired identification these criteria may also take advantage of a possible sparsity of the matrix together with the algorithms that are proposed various illustrative numerical examples are provided

a new iterative criterion for h matrices the reducible case abstract h matrices appear in various areas of science and engineering and it is of vital importance to have an algorithm to identify the h matrix character of a certain matrix a c n n recently the present authors have proposed a new iterative criterion algorithm ah to completely identify the h matrix property of an irreducible matrix the present work extends the previous algorithm to cover the reducible case as well

classes of general h matrices let m a denote the comparison matrix of a square h matrix a that is m a is an m matrix h matrices such that their comparison matrices are nonsingular are well studied in the literature in this paper we study characterizations of h matrices with either singular or nonsingular comparison matrices the spectral radius of the jacobi matrix of m a and the generalized diagonal dominance property are used in the characterizations finally a classification of the set of general h matrices is obtained

self corrective iterations sci for generalized diagonally dominant matrices a suggestive indicator is proposed for predicting whether a given complex or real square matrix a is or is not a generalized diagonally dominant matrix gddm by which we mean if a can be brought into a strictly diagonally dominant matrix by post multiplying some diagonal matrix d based on the indicator three self corrective iterative algorithms sci are presented for determining if an irreducible a is or is not a gddm and at the same time delivering the matrix d in case when a is a gddm the basic idea is to push a towards being strictly diagonally dominant when the indicator suggests that a is likely a gddm or towards being off diagonally dominant otherwise among the three algorithms each has their own feature one takes the fewest number of iterations but the most amount of work per iteration one takes the most number of iterations but the least amount of work per iteration and the third one strikes a balance between the two extremes it is shown that the algorithms will terminate in finite many steps under the assumption that a has no zero entries and the comparison matrix of a is nonsingular comparing with existing methods new algorithms are more efficient as demonstrated on known difficult examples in the literature newly designed random matrices as well as matrices from the university of florida sparse matrix collection

robust distributed estimation using the embedded subgraphs algorithm we propose a new iterative distributed approach for linear minimum mean square error lmmse estimation in graphical models with cycles the embedded subgraphs algorithm esa decomposes a loopy graphical model into a number of linked embedded subgraphs and applies the classical parallel block jacobi iteration comprising local lmmse estimation in each subgraph involving inversion of a small matrix followed by an information exchange between neighboring nodes and subgraphs our primary application is sensor networks where the model encodes the correlation structure of the sensor measurements which are assumed to be gaussian the resulting lmmse estimation problem involves a large matrix inverse which must be solved in network with distributed computation and minimal intersensor communication by invoking the theory of asynchronous iterations we prove that esa is robust to temporary communication faults such as failing links and sleeping nodes and enjoys guaranteed convergence under relatively mild conditions simulation studies demonstrate that esa compares favorably with other recently proposed algorithms for distributed estimation simulations also indicate that energy consumption for iterative estimation increases substantially as more links fail or nodes sleep thus somewhat surprisingly sensor network energy conservation strategies such as low powered transmission and aggressive sleep schedules could actually prove counterproductive our results can be replicated using matlab code from www dsp rice edu software

classical invariant theory for the quantum symplectic group in this paper we establish the quantum analogues of the first and second fundamental theorem for vector invariants for the symplectic group let us briefly recall this result consider a vector space v endowed with a non degenerate antisymmetric bilinear form let sp v denote the group of isometries the first and second fundamental theorems for vector invariants for sp v tells us that any invariant polynomial function on

simple criteria for nonsingular h matrices in this paper several new simple criteria for nonsingular h matrices are obtained by making use of elements of matrices only advantages are illustrated by numerical examples and a necessary condition for nonsingular h matrices is also presented

on factor width and symmetric h matrices we define a matrix concept we call factor width this gives a hierarchy of matrix classes for symmetric positive semidefinite matrices or a set of nested cones we prove that the set of symmetric matrices with factor width at most two is exactly the class of possibly singular symmetric h matrices also known as generalized diagonally dominant matrices with positive diagonals h we prove bounds on the factor width including one that is tight for factor widths up to two and pose several open questions

is a cn n a general h matrix abstract h matrices play an important role in the theory and applications of numerical linear algebra so it is very useful to know whether a given matrix a c n n usually the coefficient of a complex linear system of algebraic equations or of a linear complementarity problem a r n n with a ii 0 for i 1 2 n in this case is an h matrix then most of the classical iterative methods for the solution of the problem at hand converge in recent years the set of h matrices has been extended to what is now known as the set of general h matrices and a partition of this set in three different classes has been made the main objective of this work is to develop an algorithm that will determine the h matrix character and will identify the class to which a given matrix a c n n belongs in addition some results on the classes of general h matrices and a partition of the non h matrix set are presented

on brauer ostrowski and brualdi sets abstract for the localization of the spectrum of the eigenvalues of a complex square matrix the classical gersgorin theorem was extended by ostrowski who used the generalized geometric mean of the row and column sums of the matrix ostrowski and brauer extended the previous idea by using generalized geometric means of products of two row and column sums finally by using the graph theory brualdi extended all of the previous ideas further by considering generalized geometric means of products of two or more than two row and column sums these localization results can also provide classes of nonsingular matrices our main aim in this work is to exploit all the above known results and determine intervals for the parameter s k s involved so that the localization of the spectrum in question as well as the determination of the associated class of nonsingular matrices are possible

comparison of three classes of algorithms for the solution of the linear complementarity problem with an h matrix abstract there are three main classes of iterative methods for the solution of the linear complementarity problem lcp in order of appearance these classes are the projected iterative methods the block modulus algorithms and the modulus based matrix splitting iterative methods which of the three classes of methods is the best one to use for the solution of a certain problem is more or less an open question despite the fact that the best method within each class is known it is pointed out that by best we mean the minimal upper bound of the norm of the matrix operator of the absolute error vector at any iteration step with respect to the norm of the absolute initial error vector note that the first and the third classes of methods are iterative ones while the second one is iterative but needs outer n and unknown number of inner iteration steps to terminate one of the main objectives of this work is to consider the solution of the lcp with an h matrix and compare and decide theoretically if possible otherwise by numerical experiments as to which of the three best methods is the best one to use in practice

a new criterion for the h matrix property for many applications it is very useful to know whether a matrix is an h matrix or not recently some iterative tests have been proposed for distinguishing h matrix in this paper we propose a new method for being able to distinguish only a scalar times column vector numerical evidence for the effectiveness of the proposed algorithm is presented

on convergence of the modulus based matrix splitting iteration method for horizontal linear complementarity problems of h matrices abstract horizontal linear complementarity problem has wide applications such as in mechanical and electrical engineering structural mechanics piecewise linear system telecommunication systems and so on in this paper we focus on the convergence conditions of the modulus based matrix splitting iteration method proposed recently for solving horizontal linear complementarity problems by the proposed theorems the assumptions on the matrix splitting and the system matrices are weakened and the convergence domain is enlarged numerical examples are presented to show the improvement

a numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit gmwb in this paper we outline an impulse stochastic control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit gmwb assuming the policyholder is allowed to withdraw funds continuously we develop a numerical scheme for solving the hamilton jacobi bellman hjb variational inequality corresponding to the impulse control problem we prove the convergence of our scheme to the viscosity solution of the continuous withdrawal problem provided a strong comparison result holds the scheme can be easily generalized to price discrete withdrawal contracts numerical experiments are conducted which show a region where the optimal control appears to be non unique

poisson structures on affine spaces and flag varieties ii the standard poisson structures on the flag varieties g p of a complex reductive algebraic group g are investigated it is shown that the orbits of symplectic leaves in g p under a fixed maximal torus of g are smooth irreducible locally closed subvarieties of g p isomorphic to intersections of dual schubert cells in the full flag variety g b of g and their zariski closures are explicitly computed two different proofs of the former result are presented the first is in the framework of poisson homogeneous spaces and the second one uses an idea of weak splittings of surjective poisson submersions based on the notion of poisson dirac submanifolds for a parabolic subgroup p with abelian unipotent radical in which case g p is a hermitian symmetric space of compact type it is shown that all orbits of the standard levi factor l of p on g p are complete poisson subvarieties which are quotients of l equipped with the standard poisson structure moreover it is proved that the poisson structure on g p vanishes at all special base points for the l orbits on g p constructed by richardson rohrle and steinberg

the matrix analogue of the scalar aor iterative method the accelerated overrelaxation aor and the generalized aor gaor iterative methods for the solution of linear systems of algebraic equations a x b a c n i n det a 0 b c n have been around for about four decades and a plethora of variations of them have been proposed in this work a novel algorithm is introduced the matrix analogue of the aor maaor iterative method which is analysed and studied the maaor method generalizes both the aor and the gaor sufficient convergence conditions for the gaor method are determined when the coefficient matrix a of the linear system to be solved is a hermitian matrix with positive diagonal elements similarly sufficient convergence conditions for the maaor method are determined when a is a nonsingular h matrix the new convergence conditions are the most general ones so far numerical examples are presented in support of the theory developed

generalized lie algebras of type an it is shown that the quantized enveloping algebra of sl n contains a generalized lie algebra defined by means of axioms similar to woronowicz s this gives rise to lie algebra like generators and relations for the locally finite part of the quantized enveloping algebra and suggests a canonical poincare birkhoff witt basis

an iterative test for h matrix abstract for many applications it is very useful to know whether a matrix is an h matrix or not harada et al proposed simple algorithm which is produced iteratively a positive diagonal matrix d in bishan li et al linear algebra appl 271 1998 179 190 this method is useful when matrix a is an h matrix and when a is not an h matrix a wasteful computation is necessary in this paper to conquer this drawback we propose a new algorithm

the influence of the marked reduced graph of a nonnegative matrix on the jordan form and on related properties a survey abstract for a nonnegative matrix p we discuss the relation of its marked reduced graph to that part of the jordan form that is associated with the perron frobenius root to the nonnegativity of the eigenvectors and generalized eigenvectors to the nonnegativity of solutions of linear equations and to the asymptotic growth of powers of the matrix results are often stated in terms of m matrices and standard results on irreducible matrices are assumed we give examples to illustrate the theorems surveyed

nonstationary extrapolated modulus algorithms for the solution of the linear complementarity problem abstract the linear complementarity problem lcp has many applications as e g in the solution of linear and convex quadratic programming in free boundary value problems of fluid mechanics etc in the present work we assume that the matrix coefficient m r n n ccccc cof the lcp is symmetric positive definite and we introduce the optimal nonstationary extrapolation to improve the convergence rates of the well known modulus algorithm and block modulus algorithm for its solution two illustrative numerical examples show that the optimal nonstationary extrapolated block modulus algorithm is far better than all the previous similar algorithms

criterions for the positive definiteness of real supersymmetric tensors the positive definiteness of an even degree homogeneous polynomial form f x plays an important role in the stability study of nonlinear autonomous systems via lyapunov s direct method in automatic control and the positive definiteness of f x is equivalent to that of an even order supersymmetric tensor which defines f x in this paper we provide some criterions for identifying the positive definiteness of an even order real supersymmetric tensor moreover an iterative algorithm for identifying the positive definiteness of an even order real supersymmetric tensor is obtained numerical examples are given to verify the corresponding results

quantization of coboundary lie bialgebras we show that any coboundary lie bialgebra can be quantized for this we prove that a etingof kazhdan quantization functors are compatible with lie bialgebra twists and b if such a quantization functor corresponds to an even associator then it is also compatible with the operation of taking coopposites we also use the relation between the etingof kazhdan construction of quantization functors and the alternative approach to this problem which was established in a previous work

backward sdes with constrained jumps and quasi variational inequalities we consider a class of backward stochastic differential equations bsdes driven by brownian motion and poisson random measure and subject to constraints on the jump component we prove the existence and uniqueness of the minimal solution for the bsdes by using a penalization approach moreover we show that under mild conditions the minimal solutions to these constrained bsdes can be characterized as the unique viscosity solution of quasi variational inequalities qvis which leads to a probabilistic representation for solutions to qvis such a representation in particular gives a new stochastic formula for value functions of a class of impulse control problems as a direct consequence this suggests a numerical scheme for the solution of such qvis via the simulation of the penalized bsdes

a note on ostrowskiʼs theorem abstract in this note a further extension of ostrowski s theorem concerning mainly complex square irreducible matrices is presented specifically classes of irreducible matrices are determined for which the classical statement if for a matrix a a i j c n n n 2 relations a i i j 1 j i n a i j j 1 j i n a j i 1 are satisfied for all i 1 2 n and for some 0 1 then a is nonsingular can hold even if all the inequalities in it turn out to be equalities

criteria for generalized diagonally dominant matrices and m matrices abstract we provide new necessary and sufficient conditions for verifying strictly generalized diagonally dominant matrices by applying the inverse of a partitioned matrix and obtain some criteria for identifying nonsingular m matrices

weakly chained matrices policy iteration and impulse control this work is motivated by numerical solutions to hamilton jacobi bellman quasi variational inequalities hjbqvis associated with combined stochastic and impulse control problems in particular we consider i direct control ii penalized and iii semi lagrangian discretization schemes applied to the hjbqvi problem scheme i takes the form of a bellman problem involving an operator which is not necessarily contractive we consider the well posedness of the bellman problem and give sufficient conditions for convergence of the corresponding policy iteration to do so we use weakly chained diagonally dominant matrices which give a graph theoretic characterization of weakly diagonally dominant m matrices we compare schemes i iii under the following examples a optimal control of the exchange rate b optimal consumption with fixed and proportional transaction costs and c pricing guaranteed minimum withdrawal benefits in variable annuities we find that one should abstain from using sche

a note on generalized diagonally dominant matrices abstract we obtain a sufficient condition for generalized diagonally dominant matrices under the assumption that a cn n is weakly diagonally dominant an equivalent condition for a to be a generalized diagonally dominant matrix is proved