iterative solution of a 3 d scattering problem from arbitrary shaped multidielectric and multiconducting bodies we present an iterative algorithm used for the computation of the scattering from arbitrary shaped bodies made of dielectric and conducting material the harmonic problem is discretized by a hybrid boundary integral method finite element method to solve the discretized linear system a modified version of a minimal residual algorithm has been developed for complex matrices it takes into account the lagrange multiplier constraint in a special way this modified version also allows the linear system to be solved for many right hand sides in an efficient manner

on the sauer xu formula for the error in multivariate polynomial interpolation use of a new notion of multivariate divided difference leads to a short proof of a formula by sauer and xu for the error in interpolation by polynomials of total degree n in d variables at a correct point set

a conditionally cancellative left continuous t norm is not necessarily continuous abstract in this paper we propose a new method for constructing non continuous t norms from a given t norm using this method we construct a family of conditionally cancellative left continuous t norms which are not continuous thus we answer an open question which is collected by klement et al problems on triangular norms and related operators fuzzy sets and systems 145 2004 471 479

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

on a class of left continuous t norms in this paper we study the subclass of left continuous t norms n which are definable by an arbitrary continuous t norm and a weak i e non necessarily involutive negation n by putting x n y 0 if x n y x n y x y otherwise thus generalizing the construction of the so called nilpotent minimum t norms we provide the characterization of weak negations compatible with a given continuous t norm and conversely which are the continuous t norms compatible with a given weak negation function

on multivariate lagrange interpolation lagrange interpolation by polynomials in several variables is studied through a finite difference approach we establish an interpolation formula analogous to that of newton and a remainder formula both of them in terms of finite differences we prove that the finite difference admits an integral representation involving simplex spline functions in particular this provides a remainder formula for lagrange interpolation of degree n of a function f which is a sum of integrals of certain n 1 st directional derivatives of f multiplied by simplex spline functions we also provide two algorithms for the computation of lagrange interpolants which use only addition scalar multiplication and point evaluation of polynomials

the triple rotation method for constructing t norms given an involutive negator n and a left continuous t norm t that either has no zero divisors or is rotation invariant we build a rotation invariant t norm from a rescaled version of t and its left right and front rotation depending on the involutive negator n and the set of zero divisors of t some reshaping of the rescaled version of t may occur during the rotation process the rescaled version of t itself can be understood as the b zoom of the newly constructed rotation invariant t norm with b the unique fixpoint of n starting with a rotation invariant t norm t there is however one important restriction the triple rotation method based on the involutive negator n will yield a t norm if and only if the companion q of t is commutative on 0 1 2 when q is not commutative on 0 1 2 there even does not exist a rotation invariant t norm with b zoom equal to t

a theory of pseudoskeleton approximations abstract let an m n matrix a be approximated by a rank r matrix with an accuracy e we prove that it is possible to choose r columns and r rows of a forming a so called pseudoskeleton component which approximates a with o e r m n accuracy in the sense of the 2 norm on the way to this estimate we study the interconnection between the volume i e the determinant in the absolute value and the minimal singular value r of r r submatrices of an n r matrix with orthogonal columns we propose a lower bound better than one given by chandrasekaran and ipsen and by hong and pan for the maximum of r over all these submatrices and formulate a hypothesis on a tighter bound

integral equation based domain decomposition method for solving electromagnetic wave scattering from non penetrable objects the integral equation ie method is commonly utilized to model time harmonic electromagnetic em problems one of the greatest challenges in its applications arises in the solution of the resulting ill conditioned matrix equation we introduce a new domain decomposition method ddm for the ie solution of em wave scattering from non penetrable objects the proposed method is a non overlapping non conformal ddm and it provides a computationally efficient and effective preconditioner for the ie matrix equations moreover the proposed approach is very suitable for dealing with multi scale electromagnetic problems since each sub domain has its own characteristics length and will be meshed independently furthermore for each sub domain we are free to choose the most effective ie sub domain solver based on its local geometrical features and electromagnetic characteristics additionally the multilevel fast multi pole algorithm mlfma is utilized to accelerate the computations of couplings between sub domains numerical results demonstrate that the proposed method yields rapid convergence in the outer krylov iterative solution process finally simulations of several large scale examples testify to the effectiveness and robustness of the proposed ie based ddm

formulating wald tests of nonlinear restrictions on montre a partir de l evidence de monte carlo que les differences dans la forme fonctionnelle des restrictions non lineaires sont importantes dans les petites tailles d echantillons

domain decomposition method using integral equations and adaptive cross approximation ie aca ddm for studying antenna radiation and wave scattering from large metallic platforms in this paper we present a new methodology for a nonoverlapping domain decomposition method using boundary integral equations and adaptive cross approximation in the frequency domain ie aca ddm this paper proposes two main novelties first the ie ddm condition number is improved with the development of a formulation based on electric field integral equation efie implementation over the entire subdomains and on a simplification of the magnetic field integral equation mfie on the interfaces as a consequence the number of matrix vector products is significantly reduced during the iterative resolution then this paper proves that the aca can be applied and efficiently implemented in ie ddm methods moreover a hierarchical lu hlu decomposition is proposed to accelerate the aca solver the ie aca ddm is very suitable for the resolution of multiple excitations and to bypass the low frequency breakdown the flexibility accuracy and efficiency of ie aca ddm are demonstrated by comparing with reference integral equation solutions and scaled mock up measurements

seemingly unrelated regressions under additive heteroscedasticity theory and share equation applications abstract we derive consistent asymptotically efficient and asymptotically normal estimators for sur systems that have additive heteroscedastic contemporaneous correlation both our estimator for the location vector and the parameters of the covariance matrix possess these properties the procedure is superior to other methods because we use gls to estimate the parameters of the covariance matrix our method also permits the use of cross equation parameter restrictions we discuss how this type of heteroscedasticity arises naturally in share equation systems and random coefficient models and how these models can be uniquely estimated with our two step estimation technique

on the fast matrix multiplication in the boundary element method by panel clustering the boundary element method bem leads to a system of linear equations with a full matrix while fem yields sparse matrices this fact seems to require much computational work for the definition of the matrix for the solution of the system and in particular for the matrix vector multiplication which always occurs as an elementary in this paper a method for the approximate matrix vector multiplication is described which requires much less arithmetical work in addition the storage requirements are strongly reduced

triangular norms position paper i basic analytical and algebraic properties we present the basic analytical and algebraic properties of triangular norms we discuss continuity as well as the important classes of archimedean strict and nilpotent t norms triangular conorms and de morgan triples are also mentioned finally a brief historical survey on triangular norms is given

generalizations to the constructions of t norms rotation annihilation construction in this paper the constructions of triangular norms are investigated specially based on weak negations which are not necessarily involutive the rotation and the rotation annihilation constructions are extended by means of these methods we can get new families of left continuous t norms compatible with weak negations given however not all weak negations are suitable for those generalized constructions to highlight it some counterexamples are given

generalized continuous and left continuous t norms arising from algebraic semantics for fuzzy logics this paper focuses on the issue of how generalizations of continuous and left continuous t norms over linearly ordered sets should be from a logical point of view taking into account recent results in the scope of algebraic semantics for fuzzy logics over chains with a monoidal residuated operation we advocate linearly ordered bl algebras and mtl algebras as adequate generalizations of continuous and left continuous t norms respectively in both cases the underlying basic structure is that of linearly ordered residuated lattices although the residuation property is equivalent to left continuity in t norms continuous t norms have received much more attention due to their simpler structure we review their complete description in terms of ordinal sums and discuss the problem of describing the structure of their generalization to bl chains in particular we show the good behavior of bl algebras over a finite or complete chain and discuss the partial knowledge of rational bl chains then we move to the general non continuous case corresponding to left continuous t norms and mtl chains the unsolved problem of describing the structure of left continuous t norms is presented together with a fistful of construction decomposition techniques that apply to some distinguished families of t norms and finally we discuss the situation in the general study of mtl chains as a natural generalization of left continuous t norms

on bivariate hermite interpolation with minimal degree polynomials a newton type approach is used to deal with bivariate polynomial hermite interpolation problems when the data are distributed in the intersections of two families of straight lines as a generalization of regular grids the interpolation operator is degree reducing and the interpolation space is a minimal degree space integral remainder formulas are given for the lagrange case then extended to the hermite case and finally used to obtain error estimates

rotation invariant t norms where triple rotation and rotation annihilation meet generalizing the notion of a zoom of a t norm not only allows to extend the triple rotation method and its corresponding decomposition but also allows to describe the interface between the triple rotation method and the rotation annihilation method an alternative view on the partition behind the rotation annihilation method is required to make both methods compatible besides zooms we also use contour lines and the companion of a t norm to concisely formulate the results

why finite element discretizations can be factored by triangular hierarchical matrices although the asymptotic complexity of direct methods for the solution of large sparse finite element systems arising from second order elliptic partial differential operators is far from being optimal these methods are often preferred over modern iterative methods this is mainly due to their robustness in this article it is shown that an approximate lu decomposition exists which can be computed in the algebra of hierarchical matrices with almost linear complexity and with the same robustness as the classical lu decomposition low precision approximations may be used for preconditioning iterative solvers as a byproduct we prove that schur complements of stiffness matrices can be approximated with almost linear complexity

on the convergence of the aca algorithm for radiation and scattering problems the adaptive cross approximation aca algorithm when used to accelerate the numerical solution of integral equations for radiation and scattering problems sometimes suffers from inaccuracies these inaccuracies occur when the aca convergence criterion which is based on an approximation of the residual relative error is prematurely satisfied this paper identifies the two sources of this problem and proposes adaptations of the algorithm that remedy them

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

a general method for constructing left continuous t norms a new method for constructing left continuous t norms is introduced and analyzed in this paper we shall construct via embedding a left continuous t norm from any countable residuated totally and densely ordered commutative integral monoid moreover we can construct a left continuous t norm from any countable totally ordered commutative integral monoid which is not necessarily densely ordered and residuated a special case the embedding of such monoids on lexicographic product spaces is investigated in detail and several examples are demonstrated the results shed some light to chang s mv algebra to a recently proposed extraordinary t norm and to the standard semantics of the recently introduced logic ii mtl of hajek

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

the h2 wavelet method abstract in the present paper we introduce the h 2 wavelet method for the fast solution of nonlocal operator equations on unstructured meshes on the given mesh we construct a wavelet basis which provides vanishing moments with respect to the traces of polynomials in the space with this basis at hand the system matrix in wavelet coordinates is compressed to o n log n relevant matrix coefficients where n denotes the number of boundary elements the compressed system matrix is computed with nearly linear complexity by using the h 2 matrix approach numerical results in three spatial dimensions validate that we succeeded in developing a fast wavelet galerkin scheme on unstructured triangular or quadrangular meshes

a saim faffa method for efficient computation of electromagnetic scattering problems a novel method is proposed through an effective combination of the subdomain adaptive integral method saim with the fast far field approximation faffa for efficient computation of electromagnetic scattering problems in the saim technique the whole perfectly electrically conducting structure is decomposed into subdomains and each subdomain is properly handled by the aim with its local cartesian grid individually a current continuity boundary condition is introduced on the interface between contiguous subdomains to guarantee the accuracy moreover the faffa technique is utilized to speed up the process of updating the modified excitation vectors numerical results show that the present hybrid method can not only significantly decrease the number of auxiliary grid points and the memory requirement of green s function matrix but also improve the convergence of the iterative process compared to the conventional aim

co rotation annihilations of residuated semigroups two new ways to construct involutive residuated semigroups are introduced in this paper namely connected and disconnected co rotation annihilations co rotation annihilations utilizes two particular kinds of residuated semigroups to construct a third one the method is suitable for constructing a large class of examples of negative rank involutive fl e algebras that is where the unit element of the algebra is smaller than the falsum constant which defines the involution in the algebra

a multisolver scheme based on robin transmission conditions for electromagnetic modeling of highly complex objects a multisolver scheme based on robin transmission conditions rtcs is proposed for electromagnetic modeling of highly complex objects different from the traditional finite element boundary integral fe bi method that applies bi equations to truncate the fe domain the proposed multisolver scheme employs both fe and bi equations to model an object along with its background to be specific the entire computational domain consisting of the object and its background is first decomposed into multiple nonoverlapping subdomains with each modeled by either an fe or bi equation the equations in the subdomains are then coupled into a multisolver system by enforcing the rtc at the subdomain interfaces finally the combined system is solved iteratively with the application of an extended preconditioner based on an absorbing boundary condition and the multilevel fast multipole algorithm to obtain an accurate solution both the rao wilton glisson and the buffa christiansen functions are employed as the testing functions to discretize the bi equations this scheme is applied to a variety of benchmark problems and the scattering from an aircraft with a launched missile to demonstrate its accuracy versatility and capability the proposed scheme is compared with the multisolver scheme based on combined field integral equations to illustrate the differences between the two schemes

optimized numerical evaluation of singular and near singular potential integrals involving junction basis functions in analyzing conducting bodies composed of surfaces connected to wires via a method of moments discretization of the electric field integral equation junction basis functions are defined at connection points between wires and surfaces to correctly capture the physics of the current flux in the vicinity of the junction in evaluating the associated self term vector potential surface integrals two singularities are present one is related to the green s function and the other is due to the 1 behavior of the junction basis function that models the current near a junction here we present a simple and efficient numerical procedure for evaluating singular and near singular source vector potential integrals involving junction basis functions the approach is based on a double transformation that cancels both singularities and also overcomes some limitations of singularity subtraction methods the proposed scheme is then optimized to obtain at least four correct digits in the evaluation of these integrals essentially arbitrary accuracy is achievable by suitably increasing the quadrature order

a fast bie iteration method for an arbitrary body in a flow of incompressible inviscid fluid the paper is concerned with the new iteration algorithm to solve boundary integral equations arising in boundary value problems of mathematical physics the stability of the algorithm is demonstrated on the problem of a flow around bodies placed in the incompressible inviscid fluid with a discrete numerical treatment we approximate the exact matrix by a certain toeplitz one and then apply a fast algorithm for this matrix on each iteration step we illustrate the convergence of this iteration scheme by a number of numerical examples both for hard and soft boundary conditions it appears that the method is highly efficient for hard boundaries being much less efficient for soft boundaries

inexact data sparse boundary element tearing and interconnecting methods the boundary element tearing and interconnecting beti methods have recently been introduced as boundary element counterparts of the well established finite element tearing and interconnecting feti methods in this paper we present inexact data sparse versions of the beti methods which avoid the elimination of the primal unknowns and dense matrices however instead of symmetric and positive definite systems we finally have to solve twofold saddle point problems the proposed iterative solvers and preconditioners result in almost optimal solvers whose complexity is proportional to the number of unknowns on the skeleton up to some polylogarithmical factor moreover the solvers are robust with respect to large coefficient jumps

a characterization theorem on the rotation construction for triangular norms the rotation construction for t norms is introduced in j appl non classical logics 10 2000 83 92 in the present paper we characterize the widest class of operators with which the rotation construction results in left continuous t norms with involutive associated negations

continuity of left continuous triangular norms with special associated negations abstract first we show that the class of left continuous triangular norms whose associated negations are discontinuous only at one point is not generally continuous except for the trivial case second we find the strongest left continuous triangular norm with a given associated negation and shows that there is no weakest left continuous triangular norm with a given associated negation

testing for granger causality in large mixed frequency vars abstract we analyze granger causality testing in a mixed frequency var where the difference in sampling frequencies of the variables is large implying parameter proliferation problems in case we attempt to estimate the model unrestrictedly we propose several tests based on reduced rank restrictions including bootstrap versions thereof to account for factor estimation uncertainty and improve the finite sample properties of the tests and a bayesian var extended to mixed frequencies we compare these methods to a test based on an aggregated model the m a x test ghysels et al 2016a and an unrestricted var based test ghysels et al 2016b using monte carlo simulations an empirical application illustrates the techniques

combining kronecker product approximation with discrete wavelet transforms to solve dense function related linear systems a new solution technique is proposed for linear systems with large dense matrices of a certain class including those that come from typical integral equations of potential theory this technique combines kronecker product approximation and wavelet sparsification for the kronecker product factors the user is only required to supply a procedure for computation of each entry of the given matrix the main sources of efficiency are the incomplete cross approximation procedure adapted from the mosaic skeleton method of the second author and data sparse preconditioners the incomplete lu decomposition with dynamic choice of the fill in structure with a prescribed threshold and the inverse kronecker product preconditioner constructed for the sum of kronecker products of sparsified finger like matrices computed by the discrete wavelet transform in some model but quite representative examples the new technique allowed us to solve dense systems with more than 1 million unknowns in a few minutes on a personal computer with 1 gbyte operative memory

a multi solver scheme based on combined field integral equations for electromagnetic modeling of highly complex objects a combined field integral equation cfie based multisolver scheme is presented for electromagnetic modeling of objects with complex structures and materials in this scheme an object is decomposed into multiple bodies based on its material property and geometry to model bodies with complicated materials the finite element boundary integral fe bi method is applied to model bodies with homogeneous or conducting materials the method of moments is employed specifically three solvers are integrated in this multi solver scheme the fe bi cfie for inhomogeneous objects the cfie for dielectric objects and the cfie for conducting objects a mixed testing scheme that utilizes both the rao wilton glisson and the buffa christiansen functions is adopted to obtain a good accuracy in the iterative solution of the combined system the multilevel fast multipole algorithm is applied to accelerate computation and reduce memory costs and a preconditioner based on an absorbing boundary condition is employed to speed up the convergence in the numerical examples the individual solvers are first demonstrated to be well conditioned and highly accurate then the validity of the proposed multisolver scheme is demonstrated and its capability is shown by solving scattering problems of electrically large missilelike objects

evaluation of galerkin integrals involving triangular type wire to surface junctions in the method of moments the objective of this paper is to provide efficient and reliable numerical procedures for the evaluation of the galerkin testing integrals with the use of the triangular type wire to surface junction function the 1 spl rho singular behavior of the testing integrands is removed before the evaluation leading to two dimensional integrations suited for its numerical implementation compact closed form approximations are also given that allows to speed up the computations while maintaining a high level of accuracy the proposed procedure guarantees the reliable application of the galerkin s formulation to the analysis of arbitrary configurations of wires and surfaces using the rao wilton glisson basis functions for surfaces and its counterparts for wires and wire to surface junctions

black box approximation of tensors in hierarchical tucker format we derive and analyse a scheme for the approximation of order d tensors a rn1 nd in the hierarchical h tucker format a dimension multilevel variant of the tucker format and strongly related to the tt tensor train format for a fixed rank parameter k the storage complexity of a tensor in h tucker format is odk3 k i 1dni and we present a heuristic algorithm that finds an approximation to a tensor in the h tucker format in odk4 log d k2 i 1dni by inspection of only odk3 log d k2 i 1dni entries under mild assumptions tensors in the h tucker format are reconstructed for general tensors we derive error bounds that are based on the approximability of matrices matricizations of the tensor by few outer products of its rows and columns the construction parallelizes with respect to the order d and we also propose an adaptive approach that aims at finding the rank parameter for a given target accuracy e automatically

structure of left continuous triangular norms with strong induced negations iii construction and decomposition this paper is the continuation of jenei j appl non classical logics 10 2000 83 92 11 2001 351 366 where the rotation construction and the rotation annihilation construction have been presented respectively both constructions produce left continuous but not continuous triangular norms with strong induced negations here we show that these two constructions allow us to define indecomposability and that each decomposable left continuous triangular norm with strong induced negation can be derived as result of one of the above constructions in this way two general decomposition theorems arise in addition the decomposition of left continuous triangular norms with strong induced negations can be defined in a unique way namely when the decomposition is done by the minimal decomposition point