查看更多>>摘要：Invariance transformations of polyadic decompositions of matrix multiplication tensors define an equivalence relation on the set of such decompositions. In this paper, we present an algorithm to efficiently decide whether two polyadic decompositions of a given matrix multiplication tensor are equivalent. With this algorithm, we analyze the equivalence classes of decompositions of several matrix multiplication tensors. This analysis is relevant for the study of fast matrix multiplication as it relates to the question of how many essentially different fast matrix multiplication algorithms there exist. This question has been first studied by de Groote, who showed that for the multiplication of 2 x2 matrices with 7 active multiplications, all algorithms are essentially equivalent to Strassen's algorithm. In contrast, the results of our analysis show that for the multiplication of larger matrices (e.g., 2 x3 by 3 x2 or 3 x3 by 3 x3 matrices), two decompositions are very likely to be essentially different. We further provide a necessary criterion for a polyadic decomposition to be equivalent to a polyadic decomposition with integer entries. Decompositions with specific integer entries, e.g., powers of two, provide fast matrix multiplication algorithms with better efficiency and stability properties. This condition can be tested algorithmically and we present the conclusions obtained for the decompositions of small/medium matrix multiplication tensors. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this article, we present and analyze a weak Galerkin finite element method (WG-FEM) for the coupled Navier-Stokes/temperature (or Boussinesq) problems. In this WG-FEM, discontinuous functions are applied to approximate the velocity, temperature, and the normal derivative of temperature on the boundary while piecewise constants are used to approximate the pressure. The stability, existence and uniqueness of solution of the associated WG-FEM are proved in detail. An optimal a priori error estimate is then derived for velocity in the discrete H-1 and L-2 norms, pressure in the L-2 norm, temperature in the discrete H-1 and L-2 norms, and the normal derivative of temperature in H-1/2 norm. Finally, to complete this study some numerical tests are presented which illustrate that the numerical errors are consistent with theoretical results. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We derive the Laplace transforms for the prices and deltas of the powered call and put options, as well as for the price and delta of the capped powered call option under a general framework. These Laplace transforms are expressed in terms of the transform of the underlying asset price at maturity. For any model that can derive the transform of the underlying asset price, we can obtain the Laplace transforms for the prices and deltas of the powered options and the capped powered call option. The prices and deltas of the powered options and the capped powered call option can be computed by numerical inversion of the Laplace transforms. Models to which our method can be applied include the geometric Levy model, the regime-switching model, the Black- Scholes-Vasicek model, and Heston's stochastic volatility model, which are commonly used for pricing of financial derivatives. In this paper, numerical examples are presented for all four models. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the theory of functional connections. This is done without using the traditional Lagrange multiplier technique. In particular, two distinct expressions (fully satisfying the equality constraints) are provided, to first solve the constrained quadratic programming problem as an unconstrained one for closed-form solution. Such expressions are derived by utilizing an optimization variable vector, which is called the free vector g by the theory of functional connections. In the spirit of this theory, for the equality constrained nonlinear programming problem, its solution is obtained by the Newton's method combining with elimination scheme in optimization. Convergence analysis is supported by a numerical example for the proposed approach.(C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider the eigenvalue problem of a class of infinite complex symmetric tridiagonal matrices whose diagonal and off-diagonal elements diverge in modulus, and which have a compact inverse. We regard the matrix as a linear operator mapping a maximal domain in Hilbert space l(2) into l(2). This paper aims to extend the work of Ikebe et al. on a class of eigenvalue problems and for which asymptotic error estimates have been obtained. In this paper we focus on the following points: (1) considering what class of zero finding problems of three-term recurrence relations can be reformulated as eigenvalue problems of the class of infinite tridiagonal matrices stated above; (2) determining a class of matrices for which obtaining good approximate eigenvalues is guaranteed by using those of truncated principal sub-matrices; and (3) determining a class of matrices that permits us the asymptotic error estimates computed as in (2). (C)& nbsp;& nbsp;2021 The Author(s). Published by Elsevier B.V.& nbsp;& nbsp;
查看更多>>摘要：The main purpose of this article is to solve the pantograph Volterra delay integrodifferential equation of fractional order. A numerical operational matrix approach based on Euler wavelets is proposed. For the proposed scheme, the fractional integral operational matrix is constructed. Then the pantograph Volterra delay integro-differential equations are reduced to algebraic equations by using the fractional integral operational matrix. Several theorems are presented to establish the convergence and error analysis of the proposed method. To show the accuracy of the proposed technique, the numerical convergence rate has been shown. Additionally, some numerical problems are solved to justify the applicability and validity of the presented technique. Also, the numerical results have been documented graphically to describe the effectiveness of the approach. Furthermore, comparing numerical results with those obtained by known methods shows that the approach scheme is more efficient and accurate. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial splines, the related parametric curves exhibit the desired properties of convex hull inclusion, variation diminution and intuitive relation between the curve shape and the location of the control points. For a good-for-design space, in this paper we construct a set of functions, called transition functions, which allow for efficient computation of the B-spline basis, even in the case of nonuniform and multiple knots. Moreover, we show how the spline coefficients of the representations associated with a refined knot partition and with a raised order can conveniently be expressed by means of transition functions. This result allows us to provide effective procedures that generalize the classical knot insertion and degree raising algorithms for polynomial splines. We further discuss how the approach can straightforwardly be generalized to deal with geometrically continuous piecewise Chebyshevian splines as well as with splines having section spaces of different dimensions. From a numerical point of view, we show that the proposed evaluation method is easier to implement and has higher accuracy than other existing algorithms. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper proposes a new efficient operator splitting method for option pricing problem under the Heston model, which is very popular in financial engineering. The key idea of this method is relying on eliminating the cross derivative term in partial differential equation in two dimension by some variable transformation techniques, and then decomposes the original equation in two dimensions into two partial differential equations in one dimension, which can be numerically solved efficiently. Moreover, this method not only keeps the differentiability of model parameters, but also preserves the positivity, monotonicity and convexity of the option prices. Numerical results for a European put option show that this method achieves accuracy of second-order in space and first-order in time, which are coinciding with the theoretical analysis results. Since the algorithm of this paper can be parallelized easily, the option pricing problems in high-dimension can also be dealt with, such as the Basket option written on several assets and etc. Our method can also be applied to pricing American options, Asian options and option pricing problems in stochastic interest-rate models. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Compressed sensing magnetic resonance imaging (CS-MRI) makes it possible to shorten data acquisition time substantially. The traditional iteration-based CS-MRI method is flexible in modeling but is usually time-consuming. Recently, the deep neural network method becomes popular in CS-MRI due to its high efficiency. However, the drawback of the deep learning method is inflexibility. It depends overly on the training images and scanning method of the k-space data. In this paper, we propose an iterative method for MRI reconstruction, called IDPCNN, combining the merits of both the traditional method and the deep learning methods, realizing quick, flexible, and accurate reconstruction. The proposed method incorporates two stages: denoising and projection. The denoising step employs a state-of-the-art denoiser to smooth the image. The projection step explores the prior information from the frequency domain and adds details to the spatial domain iteratively. The reconstruction quality is superior to the best MRI reconstruction methods under different sampling masks and rates. The stability, speed, and good reconstruction quality mean that our IDPCNN has the potential for widespread clinical applications. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we develop and analyze a rigorous multiscale upscaling method for dual continuum model, which serves as a powerful tool in subsurface formation applications. Our proposed method is capable of identifying different continua and capturing non-local transfer and effective properties in the computational domain via constructing localized multiscale basis functions. The construction of the basis functions consists of solving local problems defined on oversampling computational region, subject to the energy minimizing constraints that the mean values of the local solution are zero in all continua except for the one targeted. The basis functions constructed are shown to have good approximation properties. It is shown that the method has a coarse mesh dependent convergence. We present some numerical examples to illustrate the performance of the proposed method. (c) 2021 Published by Elsevier B.V.
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