fast fourier transforms of piecewise constant functions we present an algorithm for the evaluation of the fourier transform of piecewise constant functions of two variables the algorithm overcomes the accuracy problems associated with computing the fourier transform of discontinuous functions in fact its time complexity is o n2 logn np log2 1 v log3 1 where is the accuracy n is the size of the problem p is the perimeter of the set of discontinuities and v is its number of vertices the algorithm is based on the lagrange interpolation formula and the green s theorem which are used to preprocess the data before applying the fast fourier transform it readily generalizes to higher dimensions and to piecewise smooth functions

a bias correction method for identification of linear dynamic errors in variables models this paper considers the problem of identifying linear systems where the input is observed in white noise but the output is observed in colored noise which also includes process disturbances an efficient method is developed which can perform unbiased parameter estimation without utilizing a prefilter the developed method is characterized by attractive features direct use of the observed data without prefiltering no need to evaluate autocorrelation functions for the input noise no need to identify a high order augmented system and provision of a direct unbiased estimate of the system parameters without parameter extraction computer simulations are presented to illustrate its superior performance including its significantly reduced computational complexity

a fast directional algorithm for high frequency electromagnetic scattering this paper is concerned with the fast solution of high frequency electromagnetic scattering problems using the boundary integral formulation we extend the o nlogn directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case we also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm when combined with a standard iterative method this results in an almost linear complexity solver for the combined field integral equations in addition the butterfly algorithm is utilized to compute the far field pattern and radar cross section with o nlogn complexity

a highly accurate fgg fg fft for the combined field integral equation in this paper a novel realization of the integral equation in combination with the fast fourier transform for the cfie is established by fitting both the green s function and its gradient onto the nodes of a uniform cartesian grid the new method has been compared with several existing popular fft based methods including the aim the ie fft and the p fft the accuracy of the proposed method is significantly higher than other fft based methods and the method is not sensitive to both the grid spacing and the expansion order the outstanding merit of the proposed method is that the fitting procedure is independent of the basis functions therefore when the higher order basis functions would be adopted in the method of moments only one fitting procedure for the green s function and its gradient on a basis function support is needed to meet all of basis functions defined on this support some numerical examples are provided in this paper to demonstrate the accuracy and efficiency of the proposed method

brief paper accuracy analysis of bias eliminating least squares estimates for errors in variables systems the bias eliminating least squares bels method is one of the consistent estimators for identifying dynamic errors in variables systems in this paper we investigate the accuracy properties of the bels estimates an explicit expression for the normalized asymptotic covariance matrix of the estimated parameters is derived and supported by some numerical examples

errors in variables identification using maximum likelihood estimation in the frequency domain this paper deals with the identification of errors in variables eiv models corrupted by additive and uncorrelated white gaussian noises when the noise free input is an arbitrary signal not required to be periodic in particular a frequency domain maximum likelihood ml estimator is proposed and analyzed in some detail as some other eiv estimators this method assumes that the ratio of the noise variances is known the estimation problem is formulated in the frequency domain it is shown that the parameter estimates are consistent an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is derived the possibility to effectively use lowpass filtered data by using only part of the frequency domain is discussed analyzed and illustrated

the frisch scheme in dynamic system identification abstract the use of the frisch scheme in the identification of linear dynamic systems is investigated in order to describe the whole family of models that can explain given input output noisy sequences unlike the algebraic case it is shown that in general only a single model is compatible with the data these results are first proposed for single input single output systems and then generalized to the multivariable case

covariance matching for continuous time errors in variables problems a covariance matching approach for continuous time errors in variables problems is considered the noise free input signal is not explicitly modeled and is only assumed to be a stationary process it is described how three different systems of equations in the model parameters are obtained and how the parameters are estimated based on these systems of equations the approach is illustrated by some numerical studies

analysis of moments based methods for fractional gaussian noise estimation fractional gaussian noise given as the increment of fractional brownian motion is a stationary gaussian process characterized by the hurst parameter in the paper moments based estimators of the hurst parameter are presented and analyzed with respect to asymptotic variance

accuracy analysis of the frisch scheme for identifying errors in variables systems several estimation methods have been proposed for identifying errors in variables systems where both input and output measurements are corrupted by noise one of the promising approaches is the so called frisch scheme this paper provides an accuracy analysis of the frisch scheme applied to system identification the estimates of the system parameters and the noise variances are shown to be asymptotically gaussian distributed an explicit expression for the covariance matrix of the asymptotic distribution is given as well numerical simulations support the theoretical results a comparison with the cramer rao lower bound is also given in the examples and it is shown that the frisch scheme gives a performance close to the cramer rao bound for large signal to noise ratios snrs

weighted ordinal means the concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied based on the relevant results on the scale 0 1 new types of weighted ordinal means are proposed in some cases these ordinal means coincide with those proposed by godo and torra but not in the case when ordinal means introduced by them are not idempotent based on divisible ordinal t conorms and modifying the approach of godo and torra we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t conorms on 0 1 and divisible ordinal t conorms

on the accuracy of a covariance matching method for continuous time errors in variables identification on the accuracy of a covariance matching method for continuous time errors in variables identification

large eddy simulation of turbulent channel flows with conservative ido scheme the resolution of a numerical scheme in both physical and fourier spaces is one of the most important requirements to calculate turbulent flows a conservative form of the interpolated differential operator ido cf scheme is a multi moment eulerian scheme in which point values and integrated average values are separately defined in one cell since the ido cf scheme using high order interpolation functions is constructed with compact stencils the boundary conditions are able to be treated as easy as the 2nd order finite difference method fdm it is unique that the first order spatial derivative of the point value is derived from the interpolation function with 4th order accuracy and the volume averaged value is based on the exact finite volume formulation so that the ido cf scheme has higher spectral resolution than conventional fdms with 4th order accuracy the computational cost to calculate the first order spatial derivative with non uniform grid spacing is one third of the 4th order fdm for a large eddy simulation les we use the coherent structure model csm in which the model coefficient is locally obtained from a turbulent structure extracted from a second invariant of the velocity gradient tensor and the model coefficient correctly satisfies asymptotic behaviors to walls the results of the ido cf scheme with the csm for turbulent channel flows are compared to the fdm with the csm and dynamic smagorinsky model as well as the direct numerical simulation dns by moser et al adding the sub grid scale stress tensor of les to the ido cf scheme improves the profile of the mean velocity in comparison with an implicit eddy viscosity of the ido cf upwind scheme the ido cf scheme with the csm gives better turbulent intensities than conventional fdms with the same number of grid points the turbulent statistics calculated by ido cf scheme are in good agreement with the dns at the various values of reynolds number re t 180 395 and 590 it is found that the ido cf scheme is suitable for the turbulent flow computation and improves the turbulent statistics with compact stencils

errors in variables system identification using structural equation modeling errors in variables eiv identification refers to the problem of consistently estimating linear dynamic systems whose output and input variables are affected by additive noise various solutions have been presented for identifying such systems in this study eiv identification using structural equation modeling sem is considered two schemes for how eiv single input single output siso systems can be formulated as sems are presented the proposed formulations allow for quick implementation using standard sem software by simulation examples it is shown that compared to existing procedures here represented by the covariance matching cm approach sem based estimation provide parameter estimates of similar quality

exact integrations of polynomials and symmetric quadrature formulas over arbitrary polyhedral grids this paper is concerned with two important elements in the high order accurate spatial discretization of finite volume equations over arbitrary grids one element is the integration of basis functions over arbitrary domains which is used in expressing various spatial integrals in terms of discrete unknowns the other consists of quadrature approximations to those integrals only polynomial basis functions applied to polyhedral and polygonal grids are treated here nontriangular polygonal faces are subdivided into a union of planar triangular facets and the resulting triangulated polyhedron is subdivided into a union of tetrahedra the straight line segment triangle and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices results are given both in terms of tensor products and products of cartesian coordinates the exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains using a coordinate free formulation simple and rational procedures are developed to derive virtually all quadrature formulas including some previously unpublished four symmetry groups of quadrature points are introduced to derive gauss formulas while their limiting forms are used to derive lobatto formulas representative gauss and lobatto formulas are tabulated the relative efficiency of their application to polyhedral and polygonal grids is detailed the extension to higher degrees of precision is discussed

refining aggregation operator based orderings in multifactorial evaluation part i continuous scales aggregation operators are often needed when building preference relations in multicriteria decision making problems most existing approaches have limitations due to incomparability between decisions or ties due to the use of some aggregation operations that produce a ranking the natural way of overcoming the lack of discrimination power is to refine the obtained ranking we bring an overview of methods that enable aggregation based rankings to be refined generalizing concepts like discrimin max leximin max and lorentz orderings that refine such aggregation operations like the minimum the maximum and the sum

fast fourier transform for discontinuous functions in computational electromagnetics and other areas of computational science and engineering fourier transforms of discontinuous functions are often required we present a fast algorithm for the evaluation of the fourier transform of piecewise smooth functions with uniformly or nonuniformly sampled data by using a double interpolation procedure combined with the fast fourier transform fft algorithm we call this the discontinuous fft algorithm for n sample points the complexity of the algorithm is o spl nu np spl nu nlog n where p is the interpolation order and spl nu is the oversampling factor the method also provides a new nonuniform fft algorithm for continuous functions numerical experiments demonstrate the high efficiency and accuracy of this discontinuous fft algorithm

a generalized instrumental variable estimation method for errors in variables identification problems the errors in variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise several estimation methods have been proposed for identifying dynamic errors in variables models in this paper it is shown how a number of common methods for errors in variables methods can be put into a general framework resulting into a generalized instrumental variable estimator give various computational aspects of give are presented and the asymptotic distribution of the parameter estimates is derived

transfer stable aggregation functions on finite lattices abstract the paper by z kurac 2019 deals with a new property the so called transfer stability characterizing the arithmetic mean with this property it is possible to define special forms of arithmetic mean on finite chains the idempotence property was required for this definition in this paper we neglect this necessity and deal only with transfer stable aggregation functions thanks to this fact it is possible to define these aggregation functions on any finite lattice hereinafter lattice and not only on finite chains transfer stable aggregation functions can be defined on any finite lattice nevertheless there is a subclass of finite lattices the so called transfer stable lattices where the behavior of the transfer stable aggregation functions is simply described because the transfer stability classes are linearly ordered therefore the main goal of this paper is characterization of these transfer stable lattices the second half of the paper deals with some useful properties associated with the lattice of all k ary transfer stable aggregation functions

non parametric identification of viscoelastic materials from wave propagation experiments we investigate how the frequency dependent wave propagation coefficient and complex modulus for a linearly viscoelastic material can be estimated from wave propagation experiments the strains at different sections of a bar specimen are measured as functions of time the time series are transformed into the frequency domain where a non parametric identification is made a thorough analysis of the quality of the non parametric estimate is made in which approximate expressions for the covariance matrices of the wave propagation coefficient and the complex modulus are derived the validity of these expressions are confirmed by numerical studies and real experiments

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

transfer stable means on finite chains abstract according to 5 the arithmetic mean is a function characterized by four features it is non decreasing idempotent symmetric and additive the first three of them can be naturally converted to the theory of posets but the last one generally can not due to this problem we will replace it with another suitable property which is called transfer stability however we do not get the exact arithmetic mean but some approximation these functions will be called transfer stable means the first aim of the paper is to show that transfer stable means on a finite chain form a lattice which is isomorphic to the direct power of a finite chain the second goal is to create a generating set of transfer stable means i e means that can generate all other transfer stable means of the same arity by classical composition of functions the last goal deals with question of how to generate all transfer stable means of any arity by binary transfer stable means only for this problem we define special transfer stable means composition

the regular fourier matrices and nonuniform fast fourier transforms for any triple of positive integers m n q the matrix f m n q called the m n q regular fourier matrix is defined the regular fourier matrices f m n q are then applied to set up new algorithms for nonuniform fast fourier transforms numerical results show that the accuracies obtained by our algorithms are much better than previously reported results with the same computation complexity the algorithms require o n cdot log 2n arithmetic operations where n is the number of data points

extended accuracy analysis of a covariance matching approach for identifying errors in variables systems a system identification method for errors in variables problems based on covariance matching was recently proposed in the first step a small amount of covariances of noisy input output data are computed and then a parametric model is fitted to these covariances in this paper the method is further analyzed and the asymptotic accuracy of the parameter estimates is derived an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is given and the identification method is shown to be asymptotically statistically efficient assuming that the given information is the computed covariances as an important byproduct an efficient algorithm is presented for computing the covariance matrix of the computed input output covariances

binary generating set of the clone of idempotent aggregation functions on bounded lattices abstract in a recent paper botur et al 2018 we have presented a generating set of the clone of idempotent aggregation functions on bounded lattices as the main result we have shown that this clone is generated by certain ternary idempotent functions from which all idempotent aggregation functions of l can be obtained by usual term composition the aim of this paper is to present an essential improvement of the result above by presenting a new generating set of this clone a bit artificial ternary functions are substituted here by natural binary lattice a medians and certain binary characteristic functions consequently the clone is generated by its binary part and the result strengthens the essential role of medians within all idempotent aggregation functions moreover we will show that for an n element lattice l the upper bound of binary generators is 2 n 1

study of mixed order basis functions for the locally corrected nystro spl uml m method a high order locally corrected nystro spl uml m lcn method employing the mixed order basis functions proposed by c 80al spl iota s 80kan and peterson is presented for the electromagnetic scattering by targets composed of both dielectric and conducting bodies an integral operator based on a combined field formulation for conducting surfaces and a mu spl uml ller formulation for dielectric surfaces is used it is found that for general scattering objects mixed order basis functions accelerate the convergence of the lcn solution can eliminate spurious charges and can significantly reduce the condition number of the impedance matrix

an accurate conformal fourier transform method for 3d discontinuous functions fourier transform of discontinuous functions are often encountered in computational electromagnetics and other areas in this work a highly accurate fast conformal fourier transform cft algorithm is proposed to evaluate the finite fourier transform of 3d discontinuous functions a curved tetrahedron mesh combined with curvilinear coordinate transform instead of the cartesian grid is adopted to flexibly model an arbitrary shape of the discontinuity boundary this enables us to take full advantages of high order interpolation and gaussian quadrature methods to achieve highly accurate fourier integration results with a low sampling density the 3d nonuniform fast fourier transform nufft helps to keep the complexity of the proposed algorithm to that similar to the traditional 3d fft algorithm therefore the proposed cft algorithm can achieve order of magnitude higher accuracy than 3d fft with lower sampling density and similar computation time the convergence is proved and verified

a spectral fc solver for the compressible navier stokes equations in general domains i explicit time stepping we present a fourier continuation fc algorithm for the solution of the fully nonlinear compressible navier stokes equations in general spatial domains the new scheme is based on the recently introduced accelerated fc method which enables use of highly accurate fourier expansions as the main building block of general domain pde solvers previous fc based pde solvers are restricted to linear scalar equations with constant coefficients the fc methodology presented in this text thus constitutes a significant generalization of the previous fc schemes as it yields general domain fc solvers for nonlinear systems of pdes while not restricted to periodic boundary conditions and therefore applicable to general boundary value problems on arbitrary domains the proposed algorithm inherits many of the highly desirable properties arising from rapidly convergent fourier expansions including high order convergence essentially spectrally accurate dispersion relations and much milder cfl constraints than those imposed by polynomial based spectral methods since for example the spectral radius of the fc first derivative grows linearly with the number of spatial discretization points we demonstrate the accuracy and optimal parallel efficiency of the algorithm in a variety of scientific and engineering contexts relevant to fluid dynamics and nonlinear acoustics

fast fourier transform based iterative method for electromagnetic scattering from 1d flat surfaces an efficient iterative method is proposed for computing the electromagnetic fields scattered from a one dimensional 1d flat surface the new iterative method is based on a similar implementation to the conjugate gradient fast fourier transform cg fft where acceleration of the matrix vector multiplications is achieved using fast fourier transforms fft however the iterative method proposed is not based on krylov subspace expansions and is shown to converge faster than gmres fft and cgne fft while maintaining the computational complexity and memory usage of those methods analysis is presented deriving an explicit convergence criterion

accelerating the nonuniform fast fourier transform the nonequispaced fourier transform arises in a variety of application areas from medical imaging to radio astronomy to the numerical solution of partial differential equations in a typical problem one is given an irregular sampling of n data in the frequency domain and one is interested in reconstructing the corresponding function in the physical domain when the sampling is uniform the fast fourier transform fft allows this calculation to be computed in o n log n operations rather than o n 2 operations unfortunately when the sampling is nonuniform the fft does not apply over the last few years a number of algorithms have been developed to overcome this limitation and are often referred to as nonuniform ffts nuffts these rely on a mixture of interpolation and the judicious use of the fft on an oversampled grid a dutt and v rokhlin siam j sci comput 14 1993 pp 1368 1383 in this paper we observe that one of the standard interpolation or gridding schemes based on gaussians can be accelerated by a significant factor without precomputation and storage of the interpolation weights this is of particular value in two and three dimensional settings saving either 10 d n in storage in d dimensions or a factor of about 5 10 in cputime independent of dimension

a covariance matching approach for identifying errors in variables systems the errors in variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise several estimation methods have been proposed for identifying dynamic errors in variables models in this paper a covariance matching approach is proposed to solve the identification problem it applies for general types of input signals the method utilizes a small set of covariances of the measured input output data this property applies also for some other methods such as the frisch scheme and the bias eliminating least squares method algorithmic details for the proposed method are provided user choices for example specification of which input output covariances to utilize are discussed in some detail the method is evaluated by using numerical examples and is shown to have competitive properties as compared to alternative methods

higher order frequency domain computational electromagnetics a review of the higher order computational electromagnetics cem for antenna wireless and microwave engineering applications is presented higher order cem techniques use current field basis functions of higher orders defined on large e g on the order of a wavelength in each dimension curvilinear geometrical elements which greatly reduces the number of unknowns for a given problem the paper reviews all major surface volume integral and differential equation electromagnetic formulations within a higher order computational framework focusing on frequency domain solutions with a systematic and unified review of generalized curved parametric quadrilateral triangular hexahedral and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions in both divergence and curl conforming arrangements a large number of actual higher order techniques representing various combinations of formulations elements bases and solution procedures are identified and discussed the examples demonstrate the accuracy efficiency and versatility of higher order techniques and their advantages over low order discretizations the most important one being a much faster higher order convergence of the solution it is demonstrated that both components of the higher order modeling namely higher order geometrical modeling and higher order current field modeling are essential for accurate and efficient cem analysis of general antenna scattering and microwave structures

brief paper relations between bias eliminating least squares the frisch scheme and extended compensated least squares methods for identifying errors in variables systems there are many methods for identifying errors in variables systems among them bias eliminating least squares bels the frisch scheme and extended compensated least squares ecls methods are attractive approaches because of their simplicity and good estimation accuracy these three methods are all based on a bias compensated least squares bcls principle in this paper the relationships between them are considered in particular the set of nonlinear equations utilized in these three methods are proved to be equivalent under different noise conditions also for finite samples it is shown that bels frisch and ecls methods have the same asymptotic estimation accuracy providing the same extended vector is used

on generating of idempotent aggregation functions on finite lattices abstract in a recent paper 9 we proposed the study of aggregation functions on lattices via clone theory approach observing that aggregation functions on lattices just correspond to 0 1 monotone clones as the main result of 9 we have shown that all aggregation functions on a finite lattice l can be obtained as usual composition of lattice operations and certain unary and binary aggregation functions the aim of this paper is to present a generating set for the class of intermediate or equivalently idempotent aggregation functions this set consists of lattice operations and certain ternary idempotent aggregation functions

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

large sample properties of separable nonlinear least squares estimators in this paper the large sample properties of the separable nonlinear least squares algorithm are investigated unlike the previous results in the literature the data are assumed to be complex valued and the whiteness assumption on the measurement noise sequence has been relaxed convergence properties of the parameter estimates are established asymptotic accuracy analysis has been carried out in which the assumptions used are relatively weaker than the assumptions in the previous related works it is shown under quite general conditions that the parameter estimates are asymptotically circular conditions for asymptotic complex normality are also established next a bound on the deviation of the asymptotic covariance matrix from the crame spl acute r rao bound crb is derived finally a sufficient condition for the nonlinear least squares estimate to achieve the crame spl acute r rao lower bound is established the results presented in this paper are general and can be applied to any specific application where separable nonlinear least squares is employed

the fast multipole method and fourier convolution for the solution of acoustic scattering on regular volumetric grids the fast multipole method fmm is applied to the solution of large scale three dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid the grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques the regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the fmm both of which scale linearly with the number of scattering elements in particular the use of fast fourier transforms to compute green s function convolutions required for neighboring interactions lowers the often significant cost of finest level fmm computations and helps mitigate the dependence of fmm cost on finest level box size numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest level box is increased

on the clone of aggregation functions on bounded lattices the main aim of this paper is to study aggregation functions on lattices via clone theory approach observing that the aggregation functions on lattices just correspond to 0 1 monotone clones as the main result we show that for any finite n element lattice l there is a set of at most 2 n 2 aggregation functions on l from which the respective clone is generated namely the set of generating aggregation functions consists only of at most n unary functions at most n binary functions and lattice operations and all aggregation functions of l are composed of them by usual term composition moreover our approach works also for infinite lattices such as mostly considered bounded real intervals a b where in contrast to finite case infinite suprema or equivalently a kind of limit process have to be considered