查看更多>>摘要：Condition number plays an important role in perturbation analysis, the latter is a tool to judge whether a numerical solution makes sense, especially for ill-posed problems. In this paper, perturbation analysis of the Tikhonov regularization of total least squares problem (TRTLS) is considered. The explicit expressions of normwise, mixed and componentwise condition numbers for the TRTLS problem are first presented. With the intermediate result, i.e. normwise condition number, we can recover the upper bound of TRTLS problem. To improve the computational efficiency in calculating the normwise condition number, a new compact and tight upper bound of the TRTLS problem is introduced. In addition, we also derive the normwise, mixed and componentwise condition numbers for TRTLS problem when the coefficient matrix, regularization matrix and right-hand side vector are all perturbed. We choose the probabilistic spectral norm estimator and the small-sample statistical condition estimation method to estimate these condition numbers with high reliability. Numerical experiments are provided to verify the obtained results. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We present an algorithm for generating approximations for the logarithm of Barnes G- function in the half-plane Re(z) >= 3/2. These approximations involve only elementary functions and are easy to implement. The algorithm is based on a two-point Pade approximation and we use it to provide two approximations to ln(G(z)), accurate to 3 x 10(-16 )and 3 x 10(-31) in the half-plane Re(z) >= 3/2; a reflection formula is then used to compute Barnes G-function in the entire complex plane. A by-product of our algorithm is that it also produces accurate approximations to the gamma function. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Volatility estimation is an important issue in certain aspects of the financial community, such as risk management and asset pricing. It is known that stock returns often exhibit volatility clustering and the tails of the distributions of these series are fatter than the normal distribution. As a response to the need of these issues, the high unconditional volatility of assets encourages the users to predict their price in an ever changing market environment. Our main focus in this paper is to study the behavior of returns and volatility dynamics of some general stochastic economic models. First, we apply the local polynomial kernel smoothing method based on nonparametric regression to estimate the mean and the variance of the returns. We then implement and develop an empirical likelihood procedure in terms of conditional variance on daily log returns for inference on the nonparametric stochastic volatility as well as to construct a confidence interval for the volatility function. It appears that the proposed algorithm is applicable to some popular financial models and represents a good fit for the behavior observed in the stock and cryptocurrency markets. Some numerical results in connection to real data on the S & P 500 index and highly volatile Bitcoin dataset are also illustrated. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we discuss the convergence of the modulus-based matrix splitting iteration methods for solving implicit complementarity problems. We simplify the iteration form of the modulus-based matrix splitting (MMS) iteration method, then propose the convergence conditions for both the simplified MMS iteration method and the modified MMS iteration method in terms of spectral radius and matrix norm. Besides, we provide the concrete convergence domains of the parameter matrix for the special case of the two methods. The corresponding numerical experiments are illustrated to show the presented results. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Burst-b distance introduced by Wainberg and Wolf (1972) has been found to be useful for correction of multiple burst errors and multiple erasures. Villalba et al. (2016) have derived extended Reiger and Singleton bound for linear code with minimum burst-b distance d(b) and then present a class of Maximum Distance Separable (MDS) codes (named as C-b code). In this paper, we derive an upper bound on d(b) for any linear code and a lower bound on d(b) for constant burst-b weight linear codes. We also present the existence of linear code with burst-b distance d(b) - 1 from code with burst distance d(b). The cardinality of a linear code and the connection of linearly independent columns of the parity check matrix of any MDS code with the distance d(b) are also given. Further, we consider periodical burst error which is found in many communication channels and investigate periodical burst-detection and -correction capability of linear codes having distance d(b). Then, we do the same investigation for C-b and its dual code C-b(perpendicular to). Finally, we give decoding procedure for the code C-b in case of periodical burst errors. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：A new concept of fuzzy improved distribution function based on fuzzy ordering defined on the support set of a given random variable is introduced. A fuzzy improved random variable based on this distribution function is defined. The existence of such a fuzzy improved random variable follows from probability integral transformation. The order statistics based on the fuzzy ordering and fuzzy improved distribution function are considered and their distributions are studied. The need for fuzzy improved order statistics arises in reliability analysis of sensitive systems where the lifetimes of the components and the system are considered by taking into account some degree of smallness defined by membership function of a fuzzy set. Examples and graphical representations of fuzzy improved distribution functions are provided.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we introduce a transformation of the center of gravity, variance and higher moments of fuzzy numbers into their possibilistic counterparts. We show that this transformation applied to the standard formulae for the computation of the center of gravity, variance, and higher moments of fuzzy numbers gives the same formulae for the computation of possibilistic moments of fuzzy numbers that were introduced by Carlsson and Fuller (2001) for the possibilistic mean and variance, and also the formulae for the calculation of higher possibilistic moments as presented by Saeidifar and Pasha (2009). We also present an inverse transformation to derive the formulae for standard measures of central tendency, dispersion, and higher moments of fuzzy numbers, from their possibilistic counterparts. This way a two-way transition between the standard and the possibilistic moments of fuzzy numbers is enabled. The transformation theorems are proven for a wide family of fuzzy numbers with continuous, piecewise monotonic membership functions. Fast computation formulae for the first four possibilistic moments of fuzzy numbers are also presented for linear fuzzy numbers, their concentrations and dilations. (C) 2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：In this paper, we consider the linearly structured partial polynomial inverse eigenvalue problem (LPPIEP) of constructing the matrices Ai is an element of Rnxn for i = 0, 1, 2, ... , (k - 1) of specified linear structure such that the matrix polynomial P(lambda) = lambda kIn + n-ary sumation k-1 has the m (1 <= m <= kn) prescribed eigenpairs as its eigenvalues and eigenvectors. Many practical applications give rise to linearly structured matrix polynomials. Typical linearly structured matrices are symmetric, skew-symmetric, tridiagonal, diagonal, pentagonal, Hankel, Toeplitz, etc. Therefore, construction of the matrix polynomial with the aforementioned structures is an important but challenging aspect of the polynomial inverse eigenvalue problem (PIEP). In this paper, a necessary and sufficient condition for the existence of solution to this problem is derived. Additionally, we characterize the class of all solutions to this problem by giving the explicit expressions of the solutions. It should be emphasized that the results presented in this paper resolve some important open problems in the area of PIEP namely, the inverse eigenvalue problems for structured matrix polynomials such as symmetric, skew-symmetric, alternating matrix polynomials as pointed out by De Teran et al. (2015). Further, we study sensitivity of solution to the perturbation of the eigendata. An attractive feature of our solution approach is that it does not impose any restriction on the number of eigendata for computing the solution of LPPIEP. Towards the end, the proposed method is validated with various numerical examples on a spring mass problem.
查看更多>>摘要：There exists the inconsistency among the design model, the analysis model, and the optimization model for the fluid cooling channel, as well as the numerical difficulty and the high computational cost caused by solving the problem of forced convection heat transfer. Our method overcomes these issues by three steps. Firstly, the seamless conversion among the three models is achieved through volume parametric reconstruction. The initial fluid cooling channel model is obtained based on some topological optimization methods, then a suitable model for isogeometric analysis (IGA) is reconstructed. Secondly, the IGA of the heat flux coupling problem is realized. To get a low-cost but sufficiently accurate analysis results, the Darcy reduced-order model is introduced when applying the IGA method, and the method is called DRIGA. After derivation of formulas for DRIGA, and applying the material properties and the boundary conditions, the problem of forced convection heat transfer is solved. With the same Darcy's reduced-order model, the calculation is finished by the finite element method (FEM), and the method is called DRFEM. Solution accuracy is studied by comparing with the solution results from the COMSOL, DRFEM and DRIGA to verify the precision and effectiveness of DRIGA. Finally, the shape optimization is realized by taking the control points on the boundary of the solid and liquid as design variables and the average temperature as objective function. After optimization, not only the average temperature is reduced, but also the boundary is continuous and smooth. The given examples show that high solution accuracy and efficient convergence can be obtained with the condition of fewer computing elements in our method. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, a backward problem for a time-space fractional diffusion equation is considered, which is to determine the initial data from a noisy final data. To deal with this ill-posed problem, combined the ideas of the Tikhonov regularization in Hilbert Schales proposed by Natterer in 1984 and the fractional Tikhonov method given by Hochstenbach-Reichel in 2011, a Tikhonov regularization method is constructed. Based on the Fourier transform, an a-priori and an a-posteriori regularization parameter choice rules are used to guarantee the order optimal convergence rates. By the finite difference methods and the Discrete Fourier transform, numerical examples in one-dimensional and two-dimensional cases are given for the a-posteriori regularization parameter choice rule. Theoretical and numerical results show that the proposed method works well for both the smooth and the non-smooth functions. (C) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier