superior properties of the presb preconditioner for operators on two by two block form with square blocks matrices or operators in two by two block form with square blocks arise in numerous important applications such as in optimal control problems for pdes the problems are normally of very large scale so iterative solution methods must be used thereby the choice of an efficient and robust preconditioner is of crucial importance since some time a very efficient preconditioner the preconditioned square block presb method has been used by the authors and coauthors in various applications in particular for optimal control problems for pdes it has been shown to have excellent properties such as a very fast and robust rate of convergence that outperforms other methods in this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs under certain conditions the condition number of the preconditioned matrix is bounded by 2 or even smaller furthermore under certain assumptions the rate of convergence is superlinear

recursive calculation of transformation factors in terms of primitive factors the authors present an algorithm for recursively calculating coupling recoupling induction and similar coefficients in terms of the primitive coefficients the algorithm is shown to be complete for any compact group they use the 6 j symbol as an example for describing their algorithm but the algorithm applies to a wide class of group theoretic transformation factors

the induction coefficient of induced representation theory its algebra and an analytic expression the induction coefficient is defined as the element of a matrix reducing the induced representation into irreducible constituents the authors give the algebra of these coefficients and a closed analytic expression in terms of matrix elements of coset representatives the consequences of this choice are derived and the importance of some of these results for the racah wigner coupling algebra of the symmetric and unitary groups noted

a parallel solver for circulant block tridiagonal systems abstract generalizing muller and scheerer s method which is used to parallelize the tridiagonal solvers this paper presents a parallel method for solving the circulant block tridiagonal systems the applications of our result to solve the block tridiagonal systems the banded systems and the circulant tridiagonal systems for example solving the closed b spline curve fitting are also addressed

an extended trapezoidal formula for the diffusion equation abstract a finite difference scheme for the diffusion equation that has enjoyed great popularity is the crank nicolson scheme 1 based on the classical trapezoidal formula for integration in time for problems with discontinuities in the boundary conditions and the initial conditions the crank nicolson scheme can give unwanted oscillations in the computed solution we present an alternative scheme based on the extended trapezoidal formula for integration in time the resulting extended trapezoidal formula finite difference scheme etf fds is third order in time unconditionally stable and unlike the crank nicolson scheme etf fds can cope with discontinuities in the boundary conditions and the initial conditions as demonstrated by the numerical examples considered

on the linear equation method for the subduction problem in symmetric groups we focus on the transformation matrices between the standard young yamanouchi basis of an irreducible representation for the symmetric group sn and the split basis adapted to the direct product subgroups we introduce the concept of subduction graph and show that it conveniently describes the combinatorial structure of the equation system arisen from the linear equation method thus we can outline an improved algorithm to solve the subduction problem in symmetric groups by a graph searching process we conclude by observing that the general matrix form for multiplicity separations resulting from orthonormalization can be expressed in terms of sylvester matrices relative to a suitable inner product in the multiplicity space

effective algorithms with circulant block matrices abstract effective numerical algorithms for circulant block matrices a whose blocks are circulant are obtained the eigenvalues of such matrices are determined in terms of the eigenvalues of matrices of reduced dimension and systems of linear equations involving these matrices are solved efficiently using fast fourier transforms

superlinearly convergent cg methods via equivalent preconditioning for nonsymmetric elliptic operators the convergence of the conjugate gradient method is studied for preconditioned linear operator equations with nonsymmetric normal operators with focus on elliptic convection diffusion operators in sobolev space superlinear convergence is proved first for equations whose preconditioned form is a compact perturbation of the identity in a hilbert space then the same convergence result is verified for elliptic convection diffusion equations using different preconditioning operators the convergence factor involves the eigenvalues of the corresponding operators for which an estimate is also given the above results enable us to verify the mesh independence of the superlinear convergence estimates for suitable finite element discretizations of the convection diffusion problems

an approximate solution for a system with a symmetric matrix abstract in this paper a large system with a symmetric and essentially 2 2 band matrix is reformulated as the product of two banded matrices for the purpose of obtaining a solution of a linear system more efficiently an error term for the approximate solution is justified in the spirit of the work by yan and chung 1

piecewise linear recursive convolution for dispersive media using fdtd electromagnetic propagation through linear dispersive media can be analyzed using the finite difference time domain fdtd method by employing the recursive convolution rc approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function the rc approach results in a fast and computationally efficient algorithm however the accuracy achieved is not generally as good as that obtained with other methods a new piecewise linear recursive convolution plrc method is described here that has greatly improved accuracy over the original rc approach but retains its speed and efficiency advantages

efficient dynamic finite element method for 3d objects with uniform cross section an efficient implicit dynamic finite element method fem for elastic 3d objects with uniform cross sections was developed in this method the finite element mesh is generated in such a way that the object to be analysed is at first sliced into layers with the same thickness along its generatrix and then each layer is discretized into finite elements of the same pattern this way of discretization makes the mass viscosity and stiffness matrices into the repetitive block tridiagonal matrices the repetitive block tridiagonal matrix has the characteristic that the sequence of matrices which appears in the gaussian elimination for the repetitive block tridiagonal matrix is a rapid convergent sequence the process of the gaussian elimination can be terminated when the sequence converges the rest of the sequence is not necessary to be stored the present method can save the computational time and memory by utilising this characteristic of the repetitive block tridiagonal matrix a few examples of analyses including whole hopkinson bar analysis were performed to demonstrate the effectiveness of the present method the present method is applicable not only to the elasto dynamics but also to many other problems such as thermal problems electrical problems and plastic problems without geometric non linearity copyright 2005 john wiley sons ltd

a new modification of the rojo method for solving symmetric circulant five diagonal systems of linear equations abstract a new effective and stable modification of the rojo method 1 for solving of real symmetric circulant five diagonal systems of linear equations is proposed this special kind of system appears in many applications spline approximation difference solution of partial differential equations etc the method presented in this paper a very efficient and stable method

split bases and multiplicity separations in symmetric group transformation coefficients we consider matrices transforming between the standard young yamanouchi basis of the symmetric group and bases adapted to the product subgroups the split basis we derive closed formulae for transformation coefficients for b 3 which includes the first cases when a choice of multiplicity separation is required we discuss considerations which can be applied to obtain a simple form for the multiplicity separation we show that the combinatorial and algebraic structure of the littlewood richardson rule also known as the biedenharn louck pattern calculus does not assist with finding a simple multiplicity separation

a new algorithm for solving nearly penta diagonal toeplitz linear systems a new numerical algorithm for solving nearly penta diagonal toeplitz linear systems is presented the algorithm is suited for implementation using computer algebra systems cass such as matlab macsyma and maple numerical examples are given in order to illustrate the efficiency of our algorithm

fast direct solution of the helmholtz equation with a perfectly matched layer or an absorbing boundary condition we consider the efficient numerical solution of the helmholtz equation in a rectangular domain with a perfectly matched layer pml or an absorbing boundary condition abc standard bilinear trilinear finite element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction type fast direct solver we present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a pml and we optimize certain parameters of the layer to minimize the reflection copyright 2003 john wiley sons ltd

efficient fdtd pml simulation of gain medium based on exponential time differencing algorithm an exponential time differencing etd algorithm is introduced to incorporate the homogeneously broadened lorentzian oscillator of gain medium in a four level atomic system into the finite difference time domain fdtd compared with the well known auxiliary differential equation ade method the proposed algorithm shows the same accuracy but can save one third of the additional memory space for treating the lorentzian oscillators and has simpler formulations the etd implementation of the stretched coordinates perfectly matched layer sc pml with the complex frequency shifted cfs stretching variable is applied to truncate computational domain with gain media simulations involving both te and tm waves indicate that compared with the modified conventional pmls and the convolution pml cpml the proposed absorbing boundary formulations can lead to a significant improvement of the absorbing performance with a similar memory requirement compared with the application of the material dependent pmls to the gain media in previous studies the proposed absorbing boundary condition has simpler formulas and can be applied to complex computational domains much more straightforwardly

the solution of linear systems equations with circulant like coefficient matrices a direct method is proposed to get the solution of linear systems of equations with circulant like coefficient matrices that find important application in engineering the elements of solutions are functions of zero points of the characteristic polynomial g z and g z of circulant matrix three examples to get the inverse matrix and the solutions of linear system are presented in the paper

a computational algorithm for solving periodic penta diagonal linear systems in this paper we present a new efficient computational algorithm for solving periodic penta digonal linear systems the implementation of the algorithm using computer algebra systems cas such as maple macsyma mathematica and matlab is straightforward an example is given in order to illustrate the algorithm

mesh independent superlinear pcg rates via compact equivalent operators the subject of the paper is the mesh independent convergence of the preconditioned conjugate gradient pcg method for nonsymmetric elliptic problems the approach of equivalent operators is involved in which one uses the discretization of another suitable elliptic operator as preconditioning matrix by introducing the notion of compact equivalent operators it is proved that for a wide class of elliptic problems the superlinear convergence of the obtained pcg method is mesh independent under finite element discretizations that is the rate of superlinear convergence is given in the form of a sequence which is mesh independent and is determined only by the elliptic operators

generating relations for reducing matrices i ordinary representations auxiliary groups are constructed that make it possible to reduce the multiplicity problem and to derive consistent generating relations for the elements of reducing matrices three examples are worked out to illustrate the general scheme

a direct method for solving circulant tridiagonal block systems of linear equations this paper presents a modification of rojo s algorithm comput math appl 20 1990 61 to solve block circulant tridiagonal systems of linear equations which are toeplitz and hermitian this new approach gives us a general direct algorithm for solving the problem we will show how to choose a block matrix as a parameter to describe the method we employ the factorization of block toeplitz tridiagonal matrices as the product of two block toeplitz subdiagonal and superdiagonal matrices the algorithm is based on obtaining the solution of the nonlinear matrix equation email protected b c 1b finally some numerical results will be given

coefficients of fractional parentage for u m p n q u m n u p q and u m n u m u n the outer product reduction coefficients orc which reduce the representation rep induced from the irreps of the permutation groups s f1 and s f2 into the irreps of s f1 f2 are shown to be the indirect coupling coefficients for the u m p n q u m n u p q irreducible basis the non standard orc for reducing the rep induced from the non standard irreps of s f13 s f1 s f3 and s f24 s f2 s f4 into that of s f s f12 s f34 with fij fi fj f f12 f34 are identified with the u f u f12 u f34 clebsch gordan coefficient for the special gel fand bases of u f12 and u f34 the u m p n q u m n u p q cfp as well as its special case the u m p u m u p cfp are identified with the s f s f12 s f34 outer product isoscalar factor the u m n u m u n cfp are obtained from the u m n u m u n cfp by simply changing all the partition labels for u n into their conjugates interchanging rows with columns and taking into account a phase change the cfp can be calculated from the orc numerical values of the one body cfp for systems with up to six particles are tabulated

symmetric and unitary group representations i duality theory an extension of the schur weyl duality connecting the representations of the symmetric and unitary groups is given the schur weyl basis is constructed using annihilation and creation operators three factorisation lemmas are derived their importance lies in the fact that they relate the phase freedoms within the racah wigner algebra of the symmetric groups and the unitary groups extensions of the regge symmetries are also given these are expressed in five duality relations

finite time balanced truncation for linear systems via shifted legendre polynomials abstract in this paper we present a finite time model order reduction method for linear systems via shifted legendre polynomials the main idea of the approach is to use finite time empirical gramians which are constructed from impulse responses by solving block tridiagonal linear systems to generate approximate balanced system for the large scale system the balancing transformation is directly computed from the expansion coefficients of impulse responses in the space spanned by shifted legendre polynomials without individual reduction of the gramians and a separate eigenvector solve then the reduced order model is constructed by truncating the states corresponding to the small approximate hankel singular values hsvs the stability preservation of the reduced model is briefly discussed and in combination with the dominant subspace projection method we modify the reduction procedure to alleviate the shortcomings of the above method which may unexpectedly lead to unstable systems even though the original one is stable furthermore the properties of the resulting reduced models are considered finally numerical experiments are given to demonstrate the effectiveness of the proposed methods

solving systems of symmetric toeplitz tridiagonal equations rojo s algorithm revisited abstract more than 20 years ago rojo published 1 an algorithm for solving linear systems where the matrix is tridiagonal symmetric toeplitz and diagonal dominant the technique proposed by rojo is very efficient o n and has been applied successfully in the solution of other similar problems circulant tridiagonal systems pentadiagonal toeplitz systems etc in this article we extend rojo s algorithm to the case of non diagonal dominant matrices thus completing a good tool in the aforementioned applications other algorithms that solve the same problem are also analysed and compared with the new version of rojo s algorithm

generating relations for reducing matrices ii corepresentations the auxiliary group approach developed in paper 1 r dirl p kasperkovitz m i aroyo j n kotzev and m angelova tjurkedjieva j math phys 27 37 1986 is generalized for the case of corepresentations of antiunitary groups it allows us to reduce the multiplicity problem and to derive consistent generating relations for the elements of the reducing matrices for coreps two examples are worked out to illustrate the general scheme

a reduced subduction graph and higher multiplicity in sn transformation coefficients transformation coefficients between standard bases for irreducible representations of the symmetric group sn and split bases adapted to the subgroup n1 n2 n are considered we first provide a selection rule and an identity rule for the subduction coefficients which allow us to decrease the number of unknowns and equations arising from the linear method by pan and chen then using the reduced subduction graph approach we may look at higher multiplicity instances as a significant example an orthonormalized solution for the first multiplicity three case which occurs in the decomposition of the irreducible representation 4 3 2 1 of s10 into 3 2 1 3 1 of s6 s4 is presented and discussed

a parallel fictitious domain method for the three dimensional helmholtz equation the application of a fictitious domain domain embedding method to the three dimensional helmholtz equation with absorbing boundary conditions is considered the finite element discretization is performed by using locally fitted meshes and an algebraic fictitious domain method with a separable preconditioner is used in the iterative solution of the resultant linear systems such a method is based on embedding the original domain into a larger one with a simple geometry with this approach it is possible to realize the gmres iterations in a low dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner an efficient parallel implementation of the iterative algorithm is introduced results of numerical experiments demonstrate good scalability properties on distributed memory parallel computers and the ability to solve high frequency acoustic scattering problems

a domain decomposition solver for acoustic scattering by elastic objects in layered media a finite element solution procedure is presented for accurately computing time harmonic acoustic scattering by elastic targets buried in sediment an improved finite element discretization based on trilinear basis functions leading to fourth order phase accuracy is described for sufficiently accurate discretizations 100 million to 1 billion unknowns are required the resulting systems of linear equations are solved iteratively using the gmres method with a domain decomposition preconditioner employing a fast direct solver due to the construction of the discretization and preconditioner iterations can be reduced onto a sparse subspace associated with the interfaces numerical experiments demonstrate capability to evaluate the scattered field with hundreds of wavelengths

solving banded and near symmetric systems in an earlier work by the authors 8 finite difference methods applied to obtain numerical approximations for the solution of nonlinear volterra integro differential equations with two point boundary conditions were considered in 8 the auxiliary conditions required to complete the system were chosen to preserve the symmetry of the banded system in general applying natural auxiliary conditions nac would give rise to a nonsymmetric banded system in this article we consider the efficient solving of a linear banded system with a near symmetric coefficient matrix

a parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension a parallel fast direct solution method for linear systems with separable block tridiagonal matrices is considered such systems appear for example when discretizing the poisson equation in a rectangular domain using the five point finite difference scheme or the piecewise linear finite elements on a triangulated possibly nonuniform rectangular mesh the method under consideration has the arithmetical complexity mathcal o n log n and it is closely related to the cyclic reduction method but instead of using the matrix polynomial factorization the so called partial solution technique is employed hence in this paper the method is called the partial solution variant of the cyclic reduction method pscr method the method is presented and analyzed in a general radix q framework and based on this analysis the radix 4 variant is chosen for parallel implementation using the mpi standard the generalization of the method to the case of arbitrary block dimension is described the numerical experiments show the sequential efficiency and numerical stability of the pscr method compared to the well known blktri implementation of the generalized cyclic reduction method the good scalability properties of the parallel pscr method are demonstrated in a distributed memory cray t3e 750 computer

integral based exponential time differencing algorithms for general dispersive media and the cfs pml two efficient integral based exponential time differencing etd algorithms for general dispersive media in the finite difference time domain fdtd are introduced the first employs a linear approximation for the field over an integral time step in the integrand denoted algorithm i and the second employs a taylor series for approximating the field over the integral time step denoted algorithm ii compared with the auxiliary differential equation ade method and the piecewise linear recursive convolution plrc method the proposed algorithms have the same second order accuracy but can lead to a substantial saving in both the memory space and cpu time consumption to complete the scheme for the open region problems a novel integral based etd implementation of the complex frequency shifted perfectly matched layer cfs pml is proposed compared with the well known recursive convolution implementation of the cfs pml cpml this new implementation can lead to a substantial saving in the cpu time and a significant improvement of around 20 db in the absorbing performance and through the integral based etd algorithm a much simpler interpretation of the cpml is presented

on the existence of positive solution for second order multi points boundary value problems here we are concerned with the existence of positive solution for autonomous and nonautonomous second order systems with multi points boundary conditions for nonautonomous systems we use the schauder s fixed point theorem in a suitable banach space while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree in order to verify the obtained results we have considered some definite systems to verify the results numerically

orientations of reflection rotation groups the authors extend the work of a previous paper 1980 in which they showed that some of the phase choices in the 3jm factors of certain point group embeddings affect the orientation of the symmetry axes the occurrence of such choices is unpredictable and their effect is sometimes subtle but once a set of 3jm factors has been calculated they can determine the orientations of the symmetry axes and mirror planes and investigate how these orientations vary with the phase choices the properties of the reflection rotation groups are obtained from the the isomorphic pure rotation groups but care is necessary in interpreting the effects of the corresponding operations of for example d3 and c3v

the inverses of some circulant matrices we present here necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three parameters and moreover we explicitly compute the inverse our study also encompasses a wide class of circulant symmetric matrices the techniques we use are related with the solution of boundary value problems associated to second order linear difference equations consequently we reduce the computational cost of the problem in particular we recover the inverses of some well known circulant matrices whose coefficients are arithmetic or geometric sequences horadam numbers among others we also characterize when a general symmetric circulant and tridiagonal matrix is invertible and in this case we compute explicitly its inverse

a parallel numerical algorithm for near symmetric and banded systems a numerical method of solution which by its nature provides approximate solutions for tridiagonal systems with toeplitz coefficient matrices is extended in two ways first the coefficient matrix is perturbed and replaced by a banded near toeplitz matrix then the algorithm is modified to allow for parallel processing the perturbations are then taken into account in two separate correction processes the convergence of the modified algorithm is examined

the symmetric group algebraic formulas for some sf 6j symbols and sf sf1 sf2 3jm symbols explicit rank dependent expressions have been obtained for some symmetric group sf 6j symbols and some sf sf1 sf2 3jm symbols using butler s recursion method a key point in deriving these results is the use of the reduced notation introduced by murnaghan to label irreps various symmetries of the 6j and 3jm symbols have been imposed these include the complex conjugation permutation and transpose conjugation we incorporate a new symmetry that arises from the occurrence of the two isomorphic direct product groups sf1 sf2 and sf2 sf1 as subgroups of sf in relation to the tables of 6j and 3jm symbols presented a discussion is given of the symmetric group unitary group duality

a fast algorithm for solving diagonally dominant symmetric pentadiagonal toeplitz systems banded toeplitz systems of linear equations arise in many application areas and have been well studied in the past recently significant advancement has been made in algorithm development of fast parallel scalable methods to solve tridiagonal toeplitz problems in this paper we will derive a new algorithm for solving symmetric pentadiagonal toeplitz systems of linear equations based upon a technique used in j m mcnally l e garey r e shaw a split correct parallel algorithm for solving tri diagonal symmetric toeplitz systems int j comput math 75 2000 303 313 for tridiagonal toeplitz systems a common example which arises in natural quintic spline problems will be used to demonstrate the algorithm s effectiveness finally computational results and comparisons will be presented

a communication less parallel algorithm for tridiagonal toeplitz systems diagonally dominant tridiagonal toeplitz systems of linear equations arise in many application areas and have been well studied in the past modern interest in numerical linear algebra is often focusing on solving classic problems in parallel in mcnally fast parallel algorithms for tri diagonal symmetric toeplitz systems mcs thesis university of new brunswick saint john 1999 an m processor split correct algorithm was presented for approximating the solution to a symmetric tridiagonal toeplitz linear system of equations nemani perturbation methods for circulant banded systems and their parallel implementation ph d thesis university of new brunswick saint john 2001 and mcnally 2003 adapted the works of rojo a new method for solving symmetric circulant tri diagonal system of linear equations comput math appl 20 1990 61 67 yan and chung a fast algorithm for solving special tri diagonal systems computing 52 1994 203 211 and mcnally et al a split correct parallel algorithm for solving tri diagonal symmetric toeplitz systems internat j comput math 75 2000 303 313 to the non symmetric case in this paper we present relevant background from these methods and then introduce an m processor scalable communication less approximation algorithm for solving a diagonally dominant tridiagonal toeplitz system of linear equations

a mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems the numerical solution of nonlinear elliptic transport systems is considered an outer inner damped inexact newton plus pcg type iteration is proposed for the finite element discretization of the problem and mesh independent superlinear convergence is proved for both the outer and inner iterations numerical experiments are enclosed

a new method for solving symmetric circulant tridiagonal systems of linear equations in this paper a new method for computing the solution of a linear system having a symmetric circulant tridiagonal matrix is presented this special kind of system appears in many applications after an appropriate partition of the system and the elimination of the last unknown we apply the woodbury formula to arrive at a very efficient and stable method which is quite competitive with gaussian elimination and with the modified double sweep method

the inverse of circulant matrix abstract a direct method is proposed to get the inverse matrix of circulant matrix that find important application in engineering the elements of the inverse matrix are functions of zero points of the characteristic polynomial g z and g z of circulant matrix four examples to get the inverse matrix are presented in the paper

calculating symmetric group split standard transformation coefficients using the block selective method a proof the split basis for the symmetric group sn is adapted to sn and to the product subgroup sn a sa the entries in the matrix that transforms between the split basis representation and the standard young yamanouchi yy basis the split standard transformation coefficients are closely related to a particle coefficients of fractional parentage recently the block selective conjecture was proposed for calculating the coefficients the conjecture implies that the transformation matrix is directly related to the representation matrix in the yy basis of a cycle permutation we present a proof of this conjecture

on cscs based iteration methods for toeplitz system of weakly nonlinear equations abstract for toeplitz system of weakly nonlinear equations by using the separability and strong dominance between the linear and the nonlinear terms and using the circulant and skew circulant splitting cscs iteration technique we establish two nonlinear composite iteration schemes called picard cscs and nonlinear cscs like iteration methods respectively the advantage of these methods is that they do not require accurate computation and storage of jacobian matrix and only need to solve linear sub systems of constant coefficient matrices therefore computational workloads and computer storage may be saved in actual implementations theoretical analysis shows that these new iteration methods are local convergent under suitable conditions numerical results show that both picard cscs and nonlinear cscs like iteration methods are feasible and effective for some cases

exponential convergence through linear finite element discretization of stratified subdomains motivated by problems where the response is needed at select localized regions in a large computational domain we devise a novel finite element discretization that results in exponential convergence at pre selected points the key features of the discretization are a use of midpoint integration to evaluate the contribution matrices and b an unconventional mapping of the mesh into complex space named complex length finite element method cfem the technique is linked to pade approximants that provide exponential convergence of the dirichlet to neumann maps and thus the solution at specified points in the domain exponential convergence facilitates drastic reduction in the number of elements this combined with sparse computation associated with linear finite elements results in significant reduction in the computational cost the paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving laplace helmholtz and elastodynamics equations

calculation of primitive 6 j symbols the 6 j symbols of a group are independent of the subgroup chain chosen to define the basis states the authors present an improved algorithm for calculating the primitive 6 j symbols for a compact group with a faithful irrep by recursive building up using only the kronecker product rules and the general properties of 6 j previously one has sometimes needed to search for the useful equations by systematically trying all equations which involve unknown 6 j the authors show that the primitive 6 j may all be easily solved in terms of a subclass the core 6 j they discuss how the core 6 j can usually be solved proving that the method is complete for so3 the authors conjecture that the algorithm is complete for all groups

su mn su m su n isoscalar factors and s f1 f2 s f1 s f2 isoscalar factors a simple relation is found between the isoscalar factor isf of the unitary group and those of the permutation group i e the su mn su m su n isf is equal to the s f1 f2 s f1 s f2 isf since the values of s f1 f2 s f1 s f2 isf are independent of m and n one arrives at an important conclusion that the values of su mn su m su n isf are also independent of m and n therefore they can be calculated for all m and n by a single stroke instead of one m and one n at a time an eigenfunction metho for evaluating the su mn su m su n isf is given which can be easily translated into a computer program

symmetries of group subgroup transformation factors for coupling subduction and induction group subgroup gh transformation theory uses g transformation coefficients and gh transformation factors to describe the relationship between the various bases of representation space of any group decomposed into irreducible representation spaces of the group and its subgroups the representation spaces may be formed by the processes of coupling subduction or induction the authors further develop this gh transformation theory with the study of the various symmetries complex conjugation transposition and associativity of the gh transformation factor emphasising the origins of each symmetry and a hierarchy within these symmetries a method of calculation is given for certain transformation factors the results and methods presented here generalise those of the racah wigner coupling algebra

3jm and 6j tables for some bases of su6 and su3 tables of 6j symbols for su6 and su3 and tables of 3jm factors for su6 contains implies su2 su3 su3 contains implies u1 su2 and su3 contains implies so3 are presented the tables are computer produced using a program that implements the building up principle in a general form these tables are useful for calculations in high energy nuclear and solid state physics some other tabulations contain errors and none uses all the symmetries available the n independence of sun results is discussed by using the various symmetric group unitary group duality relations

coupling subduction and induction transformations for group representations the basis of a representation space of any group may be chosen according to its decomposition into representations of the group and a subgroup chain coupling recoupling subduction and resubduction factors are each shown to arise as a result of schur s lemmas and a particular group subgroup structure when induction and mackey s subgroup theorem are considered new transformation factors occur those of induction and reinduction key properties of these factors are given together with their relationship with double coset matrix elements

a fast algorithm for solving toeplitz penta diagonal systems in this paper a fast algorithm for solving a large system with a symmetric toeplitz penta diagonal coefficient matrix is presented this efficient method is based on the idea of a system perturbation followed by corrections and is competitive with standard methods the error analysis is also given

simultaneity and reality of u n and su n 3jm and 6j symbols a simple proof is given of the simultaneous existence of a real set of 3jm and 6j symbols for the unitary groups u n and su n including the case of mixed tensor representations we observe that simultaneity is incompatible with the conventional permutation symmetries for u n with n 3 the relevance of these results to the schur weyl duality of u n with the symmetric groups sl is discussed

preconditioning operators and sobolevgradients for nonlinear elliptic problems a preconditioning framework is presented for the iterative solution of nonlinear elliptic problems based on the preconditioning operator approach various fixed preconditioning operators are used in the iteration which can be interpreted as a weighted sobolev gradient method

sobolev gradient preconditioning for the electrostatic potential equation sobolev gradient type preconditioning is proposed for the numerical solution of the electrostatic potential equation a constructive representation of the gradients leads to efficient laplacian preconditioners in the iteration thanks to the available fast poisson solvers convergence is then verified for the corresponding sequence in sobolev space implying mesh independent convergence results for the discretized problems a particular study is devoted to the case of a ball due to the radial symmetry of this domain a direct realization without discretization is feasible the simplicity of the algorithm and the fast linear convergence are finally illustrated in a numerical test example

3jm factors and basis functions for d h and c v the results of earlier work by butler and reid for the pure rotation double group dinfinity are used to obtain algebraic formulae for the 3jm factors of the branching dinfinity h contains implies cinfinity v other branchings involving these groups are trivially related to branchings involving dinfinity the transformations of the group chains o3 contains implies dinfinity h contains implies cinfinity h and o3 contains implies dinfinity h contains implies cinfinity v contains implies cinfinity to the standard angular momentum basis are also given

generating function of isoscalar factors of unitary groups the author introduces a new schematisation of the elements of the bases of the fundamental representations of the unitary groups using this schematisation as well as two rules which will be established in this work the author is able to find by an elementary calculation the generating function of coupling coefficients of this basis this last generating function permits the author to find the one corresponding to su n isoscalar factors the approach gives in the general case i e for every n the algebraic expressions of these factors the author shows that to find the elements of the irreducible representation of the direct product of n representations and gives the details of this method in the special case n 2 a priori the method can be easily applied to other classical groups

on the solution of circulant linear systems the solution of linear systems having circulant coefficient matrices iss considered in this paper this kind of system occurs in many applications prediction time series analysis spline approxim

superlinearly convergent pcg algorithms for some nonsymmetric elliptic systems a preconditioned conjugate gradient method is applied to finite element discretizations of some nonsymmetric elliptic systems mesh independent superlinear convergence is proved which is an extension of a similar earlier result from a single equation to systems the proposed preconditioning method involves decoupled preconditioners which yields small and parallelizable auxiliary problems

low complexity bayesian estimation of cluster sparse channels this paper addresses the problem of channel impulse response estimation for cluster sparse channels under the bayesian estimation framework we develop a novel low complexity minimum mean squared error mmse estimator by exploiting the sparsity of the received signal profile and the structure of the measurement matrix it is shown that due to the banded toeplitz circulant structure of the measurement matrix a channel impulse response such as underwater acoustic channel impulse responses can be partitioned into a number of orthogonal or approximately orthogonal clusters the orthogonal clusters the sparsity of the channel impulse response and the structure of the measurement matrix all combined result in a computationally superior realization of the mmse channel estimator the mmse estimator calculations boil down to simpler in cluster calculations that can be reused in different clusters the reduction in computational complexity allows for a more accurate implementation of the mmse estimator the proposed approach is tested using synthetic gaussian channels as well as simulated underwater acoustic channels symbol error rate performance and computation time confirm the superiority of the proposed method compared to selected benchmark methods in systems with preamble based training signals transmitted over cluster sparse channels

preconditioning for vector valued cahn hilliard equations the solution of vector valued cahn hilliard systems is of interest in many applications we discuss strategies for the handling of smooth and nonsmooth potentials as well as for different types of constant mobilities concerning the nonsmooth systems the necessary bound constraints are incorporated via the moreau yosida regularization technique we develop effective preconditioners for the efficient solution of the linear systems in saddle point form numerical results illustrate the efficiency of our approach in particular we numerically show mesh and phase independence of the developed preconditioner in the smooth case the results in the nonsmooth case are also satisfying and the preconditioned version always outperforms the unpreconditioned one

parallel algorithms for solving tridiagonal and near circulant systems many problems in mathematics and applied science lead to the solution of linear systems having circulant coefficient matrices this paper presents a new stable method for the exact solution of non symmetric tridiagonal circulant linear systems of equations the method presented in this paper is quite competitive with gaussian elimination both in terms of arithmetic operations and storage requirements it is also competitive with the modified double sweep method this method can be applied to solve the near circulant tridiagonal system in addition the method is modified to allow for parallel processing

an efficient algorithm for a model with a bidiagonal coefficient matrix bidiagonal matrices arise directly in the discretization of models using one step methods and indirectly through the factoring of tridiagonal systems with special characteristics we first look at the solution of a bidiagonal system and then relate it to an experimental method that has been used to determine the overall heat transfer coefficient in a concentric tube parallel flow heat exchanger the discretization of the governing partial differential equation with its boundary conditions gives rise to a near toeplitz bidiagonal system here we consider a method for the parallel processing of the resulting systems to provide measurements at fixed spatial and time increments

a direct method for solving block circulant banded system of linear equations abstract a direct method to solve block circulant banded system of linear equations is presented in the paper the method applies the kernel solution of linear equations with circulant banded matrix proposed by fuyong 2011 17 by using the kernel solution of linear equations with block circulant banded matrix we obtain the boundary equations of the linear equations and by solving the boundary equations of the linear systems we finally get the solution of the linear equations the proposed method has great advantage in getting solutions of linear systems with block circulant banded matrix coefficient matrices an example is presented in the paper

the aitken like acceleration of the schwarz method on nonuniform cartesian grids in this paper we present a family of domain decomposition based on an aitken like acceleration of the schwarz method seen as an iterative procedure with a linear rate of convergence this paper is a generalization of the method first introduced at the 12th international conference on domain decomposition that was restricted to regular cartesian grids the potential of this method to provide scalable parallel computing on a geographically broad grid of parallel computers was demonstrated for some linear and nonlinear elliptic problems discretized by finite differences on a cartesian mesh the main purpose of this paper is to present a generalization of the method to nonuniform cartesian meshes the salient feature of the method consists of accelerating the sequence of traces on the artificial interfaces generated by the schwarz procedure using a good approximation of the main eigenvectors of the trace transfer operator for linear separable elliptic operators our solver is a direct solver for nonlinear operators we use an approximation of the eigenvectors of the jacobian of the trace transfer operator the acceleration is then applied to the sequence generated by the schwarz algorithm applied directly to the nonlinear operator

numerical solution of the nonlinear helmholtz equation using nonorthogonal expansions in j comput phys 171 2001 632 677 we developed a fourth order numerical method for solving the nonlinear helmholtz equation which governs the propagation of time harmonic laser beams in media with a kerr type nonlinearity a key element of the algorithm was a new nonlocal two way artificial boundary condition abc set in the direction of beam propagation this two way abc provided for reflectionless propagation of the outgoing waves while also fully transmitting the given incoming beam at the boundaries of the computational domain altogether the algorithm of j comput phys 171 2001 632 677 has allowed for a direct simulation of nonlinear self focusing without neglecting nonparaxial effects and backscattering to the best of our knowledge this capacity has never been achieved previously in nonlinear optics in the current paper we propose an improved version of the algorithm the principal innovation is that instead of using the dirichlet boundary conditions in the direction orthogonal to that of the laser beam propagation we now introduce sommerfeld type local radiation boundary conditions which are constructed directly in the discrete framework numerically implementation of the sommerfeld conditions requires evaluation of eigenvalues and eigenvectors for a non hermitian matrix subsequently the separation of variables which is a key building block of the aforementioned nonlocal abc is implemented through an expansion with respect to the nonorthogonal basis of the eigenvectors numerical simulations show that the new algorithm offers a considerable improvement in its numerical performance as well as in the range of physical phenomena that it is capable of simulating

phase conventions consistent with duality between sun and sl the schur weyl construction of irreducible tensors by symmetrized lth rank exterior products of a defining n dimensional vector space establishes a duality between the coupling algebra of the unitary group un and the symmetric group sl the coupling coefficients shared by these two groups are real and possess symmetries due to complex conjugation in un and association in sl the unitary group is factored by its unitary unimodular subgroup sun un u1 so it is usual to identify the coupling algebras of un and sun by choosing the trivial phaseless coupling for u1 this establishes a set of equivalence relations since all pseudoscalar irreducible representations irreps of un subduce onto the scalar irrep of sun the question remains can this trivial identification with the coupling algebra of sun be made consistent with the symmetries which follow from duality specifically the symmetries which follow from duality must be consistent with the equivalence relations we argue such consistency may be obtaine

a parallel algorithm for solving toeplitz linear systems numerical methods of solution are considered for systems which are toeplitz and symmetric in our case the coefficient matrix is essentially tridiagonal and sparse there are two distinct approaches to be considered each of which is efficient in its own way here we will combine the two approaches which will allow application of the cyclic reduction method to coefficient matrices of more general forms the convergence of the approximations to the exact solution will also be examined solving linear systems by the adapted cyclic reduction method can be parallel processed

a parallel iterative method for solving periodical block tridiagonal linear equations abstract in this paper based upon splitting the coefficient matrix we propose a parallel iterative algorithm for periodical block tridiagonal linear equations on distributed memory multi computers which is more general applied than presented in lihua chi jie liu xiaomei li an effective parallel algorithm for tridiagonal linear equations journal of computer 22 2 1999 218 221 our algorithm can be easily generalized to solve the tridiagonal systems the block tridiagonal and the periodical block tridiagonal systems the communication only needs twice between the adjacent processors per iteration furthermore analysis of convergence and error about this algorithm is given finally some numerical results on hp r 2600 cluster show that practice computing is consistent with theory the algorithm has great parallel efficiency

algebraic formulas for some nontrivial un 6j symbols and umn um un 3jm symbols we give tables of algebraic formulas for some nontrivial 6j symbols and 3jm symbols of the unitary groups the tables demonstrate that the building up method can be used successfully to obtain the rank dependence of unitary group j and jm symbols to emphasize the rank dependent nature of this calculation we have employed the composite young tableaux notation or back to back notation to label the unitary group irreps in using this notation the transpose conjugate symmetry of the corresponding composite young diagram leads to a new symmetry of the unitary group 6j and 3jm symbols the transposition of the groups um and un gives rise to a further symmetry of the 3jm symbols of umn um un

low sampling rate ultra wideband channel estimation using equivalent time sampling in this paper a low sampling rate scheme for ultra wideband channel estimation is proposed the scheme exploits multiple observations generated by transmitting multiple pulses in the proposed scheme p pulses are transmitted to produce channel impulse response estimates at a desired sampling rate while the adc samples at a rate that is p times slower to avoid loss of fidelity the number of sampling periods based on the desired rate in the inter pulse interval is restricted to be co prime with p this condition is affected when clock drift is present and the transmitted pulse locations change to handle this case and to achieve an overall good channel estimation performance without using prior information we derive an improved estimator based on the bounded data uncertainty bdu model it is shown that this estimator is related to the bayesian linear minimum mean squared error lmmse estimator channel estimation performance of the proposed sub sampling scheme combined with the new estimator is assessed in simulation the results show that high reduction in sampling rate can be achieved the proposed estimator outperforms the least squares estimator in almost all cases while in the high snr regime it also outperforms the lmmse estimator in addition to channel estimation a synchronization method is also proposed that utilizes the same pulse sequence used for channel estimation

a second order exponential time differencing scheme for non linear reaction diffusion systems with dimensional splitting abstract a second order l stable exponential time differencing etd method is developed by combining an etd scheme with approximating the matrix exponentials by rational functions having real distinct poles rdp together with a dimensional splitting integrating factor technique a variety of non linear reaction diffusion equations in two and three dimensions with either dirichlet neumann or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second order implicit explicit schemes an additional performance boost is gained through further use of basic parallelization techniques

acceleration of the schwarz method for elliptic problems in this paper we present a family of domain decomposition methods based on aitken like acceleration of the schwarz method which is an iterative procedure with linear rate of convergence this paper is a generalization of our method first introduced in 2000 that was restricted to cartesian grids we consider the finite volume fv approximation on general quadrangle meshes introduced by faille in 1992 we first present the so called aitken schwarz procedure for a linear differential operator this solver is a direct solver but its computational cost in the general case might be prohibitive second we introduce the steffensen schwarz variant which is an iterative domain decomposition solver that can be applied to linear and nonlinear problems we show that this iterative solver has reasonable numerical efficiency and can be applied successfully to several classes of linear and nonlinear elliptic problems however the salient feature of our method is that our algorithm has high tolerance for slow networks in the context of distributed parallel computing and is attractive to use with computer architectures for which performance is limited by the memory bandwidth rather than the flop performance of the cpu this is currently the case for most parallel computers using risc processor architecture such as beowulf systems

a parallel method for linear equations with tridiagonal toeplitz coefficient matrices abstract there are many articles on symmetric tridiagonal toeplitz and circulant systems such systems in areas including numerical methods for solving boundary value differential equations and in graph theory these matrices can often be written as the product of bidiagonal matrices in this article nonsymmetric toepliz systems and nonsymmetric circulant systems are examined the coefficient matrix is split into two bidiagonal matrices and the efficient solution of the resulting systems is considered

some algorithms for solving special tridiagonal block toeplitz linear systems this paper is focused on different methods and algorithms for solving tridiagonal block toeplitz systems of linear equations we consider the el sayed method ph d thesis 1996 for such systems and propose several modifications that lead to different algorithms which we discuss in detail our algorithms are then compared with some classical techniques as far as implementation time is concerned number of operations and storage comments and conclusions for computing efficiency of the proposed new algorithms are given numerical experiments corroborating the theoretical results are also presented

iterative solution methods for modeling multiphase flow in porous media fully implicitly we discuss several fully implicit techniques for solving the nonlinear algebraic system arising in an expanded mixed finite element or cell centered finite difference discretization of two and three phase porous media flow every outer nonlinear newton iteration requires solution of a nonsymmetric jacobian linear system two major types of preconditioners supercoarsening multigrid scmg and two stage are developed for the gmres iteration applied to the solution of the jacobian system the scmg reduces the three dimensional system to two dimensions using a vertical aggregation followed by a two dimensional multigrid the two stage preconditioners are based on decoupling the system into a pressure and concentration equations several pressure preconditioners of different types are described extensive numerical results are presented using the integrated parallel reservoir simulator ipars and indicate that these methods have low arithmetical complexity per iteration and good convergence rates

a structure preserving matrix factorization for solving general periodic pentadiagonal toeplitz linear systems abstract in the current article a new algorithm for solving linear systems with the periodic pentadiagonal toeplitz ppt coefficient matrix is presented this algorithm is based on a structure preserving matrix factorization and sherman morrison woodbury formula some numerical examples are given in order to illustrate the effectiveness of the proposed algorithms all of the experiments are performed on a computer with the aid of programs written in matlab