A distributed algorithm for European options with nonlinear volatility

A distributed algorithm is developed to solve nonlinear Black-Scholes equations in the hedging of portfolios. The algorithm is based on an approximate inverse Laplace transform and is particularly suitable for problems that do not require detailed knowledge of each intermediate time steps.     

Modelling and simulation of nabla fractional dynamic systems with nonzero initial conditions

The paper focuses on the numerical approximation of discrete fractional order systems with the conditions of nonzero initial instant and nonzero initial state. First, the inverse nabla Laplace transform is developed and the equivalent infinite dimensional frequency distributed model of discrete fractional order system is introduced. Then, resorting the nabla discrete Laplace transform, the rationality of the finite dimensional frequency distributed model approaching the infinite one is illuminated. Based on this, an original algorithm to estimate the parameters of the approximate model is proposed with the help of vector fitting method. Additionally, the applicable object is extended from a sum operator to a general system. Three numerical examples are performed to illustrate the applicability and flexibility of the introduced methodology.     

Numerical solution of time-dependent component with sparse structure of source term for a time fractional diffusion equation

We consider an inverse time-dependent component of source term with sparse structure for the time fractional diffusion equation in the present paper. We prove the uniqueness of the inverse problem with nonlocal observation data by Laplace transform technique. Concerning the sparsity of the source term, we transform the inverse source problem into an elastic-net regularization optimization problem. The semi-smooth Newton method is adopted to solve the optimization problem and the superconvergence of the semi-smooth Newton algorithm is proven. Several numerical examples are tested to verify the efficiency of the algorithm.     

Solving inverse laplace transform,linear and nonlinear state equations using block-pulse functions

A recursive algorithm is developed for solving the inverse Laplace transform, linear and nonlinear state equations using block-pulse functions. The relationships between the solution of the continuous-time state equation using block-pulse functions and that of the equivalent discrete-time state equation using trapezoidal rule are investigated. A complete computer program is presented for solving the differential equations of linear and nonlinear state equations using block-pulse functions.     

Functional approximation for inversion of Laplace transforms via polynomial series

A method for finding the inverse of Laplace transforms using polynomial series is discussed. It is known that any polynomial series basis vector can be transformed into Taylor polynomials by use of a suitable transformation. In this paper, the cross product of a polynomial series basis vector is derived in terms of Taylor polynomials, and as a result the inverse of the Laplace transform is obtained, using the most commonly used polynomial series such as Legendre, Chebyshev, and Laguerre. Properties of Taylor series are first briefly presented and the required function is given as a Taylor series with unknown coefficients. Each Laplace transform is converted into a set of simultaneous linear algebraic equations that can be solved to evaluate Taylor series coefficients. The inverse Laplace transform using other polynomial series is then obtained by transforming the properties of the Taylor series to other polynomial series. The method is simple and convenient for digital computation. Illustrative examples are also given,     

Convergence Analysis of Iterative Laplace Transform Methods for the Coupled PDEs from Regime-Switching Option Pricing

This paper aims to analyze the convergence rates of the iterative Laplace transform methods for solving the coupled PDEs arising in the regime-switching option pricing. The so-called iterative Laplace transform methods are described as follows. The semi-discretization of the coupled PDEs with respect to the space variable using the finite difference methods (FDMs) gives the coupled ODE systems. The coupled ODE systems are solved by the Laplace transform methods among which an iteration algorithm is used in the computational process. Finally, the numerical contour integral method is used as the Laplace inversion to restore the solutions to the original coupled PDEs from the Laplace space. This Laplace approach is regarded as a better alternative to the traditional time-stepping method. The errors of the approach are caused by the FDM semi-discretization, the iteration algorithm and the Laplace inversion using the numerical contour integral. This paper provides the rigorous error analysis for the iterative Laplace transform methods by proving that the method has a second-order convergence rate in space and exponential-order convergence rate with respect to the number of the quadrature nodes for the Laplace inversion.     

A cooley-tukey algorithm for the slant transform

A Cooley-Tukey algorithm for the slant transform and its inverse is developed. It is shown that using this algorithm, one can compute the slant transform by means of a simple modification of the same Cooley-Tukey algorithm which is used to compute the Hadamard ordered Walsh-Hadamard transform.     

A heuristic approach to the inverse Laplace transform of higher order systems

A heuristic approach to the inverse Laplace transform of higher order systems is presented. The equation derived is compact and no matrix inversion is needed. A new recursive formula for the integral of state transition matrix exp (At) is also derived to make the algorithm complete. In addition, analog simulation of unit impulse response can be easily done through the heuristic approach. Three numerical examples are included for illustration and a complete set of computer programs in FORTRAN IV is listed in the Appendix     

Recursive computation of Tchebichef moment and its inverse transform

Tchebichef moment is a novel set of orthogonal moment applied in the fields of image analysis and pattern recognition. Less work has been made for the computation of Tchebichef moment and its inverse moment transform. In this paper, both a direct recursive algorithm and a compact algorithm are developed for the computation of Tchebichef moment. The effective recursive algorithm for inverse Tchebichef moment transform is also presented. Clenshaw's recurrence formula was used in this paper to transform kernels of the forward and inverse Tchebichef moment transform. There is no need for the proposed algorithms to compute the Tchebichef polynomial values. The approaches presented are more efficient compared with the straightforward methods, and particularly suitable for parallel VLSI implementation due to their regular and simple filter structures.     

An FFT-based algorithm for 2D power series expansions

An effective numerical algorithm based on inverting a specialized Laplace transform is derived for computing the two-dimensional power-series expansion coefficients of a two-variable function. Due to the special structure of the constructed 2D Laplace transform, the accuracy of the inverted function values can be assured effectively by the generalized Riemann zeta function evaluation and the multiple sets of 2D FFT computation. Therefore, the algorithm is particularly amenable to modern computers having multiprocessors and/or vector processors.     

Finite element analysis of a compressible dynamic viscoelastic sphere using FFT

An extension to a compressible dynamic viscoelastic hollow sphere problem with both finite and infinite outer radius is performed. The governing viscoelastic equations of motion are transformed into the Laplace domain via the elastic–viscoelastic correspondence principle. Real and imaginary parts of the nodal displacements are obtained by solving a non-symmetric matrix equation in the complex Laplace domain. Inversion into the time domain is performed using the discrete inverse Fourier transform. Use is made of an infinite element in the infinite sphere problem. Numerical solutions are compared to both the exact Laplace and time domain solutions wherever possible.     

Symbolic-numerical solution of systems of linear ordinary differential equations with required accuracy

In the paper, a symbolic-numerical algorithm for solving systems of ordinary linear differential equations with constant coefficients and compound right-hand sides. The algorithm is based on the Laplace transform. A part of the algorithm determines the error of calculation that is sufficient for the required accuracy of the solution of the system. The algorithm is efficient in solving systems of differential equations of large size and is capable of choosing methods for solving the algebraic system (the image of the Laplace transform) depending on its type; by doing so the efficiency of the solution of the original system is optimized. The algorithm is a part of the library of algorithms of the Mathpar system [15].     

Generalization and computerization of the heaviside expansion for performing the inverse laplace transform of high order systems

A complete computer program is written for performing the inverse Laplace transform of a high order transfer function. The program enables us to obtain a closed form solution and a time response curve from a high order transfer function with many high power repeated roots.     

Embedded image coding using laplace transform for Turkish letters

In this paper, a different cryptographic method is introduced by using a Power series transform. A new algorithm for cryptography is produced. The extended Laplace transform of the exponential function is used to encode an explicit text. The key is generated by applying the modular arithmetic rules to the coefficients obtained in the transformation. Here, ASCII codes used to hide the mathematically generated keys to strengthen the encryption. Text steganography is used to make it difficult to break the password. The made encryption is reinforced by image steganography. To hide the presence of the cipher text, it is embedded in another open text with a stenography method. Later, this text is buried in an image. For decryption, it is seen that the inverse of the Power series transform can be used for decryption easily. Experimental results are obtained by making a simulation of the proposed method. As a result, it is stated that the proposed method can be used in crypto machines.

     

Numerical inversion of multidimensional Laplace transforms by the Laguerre method

Numerical transform inversion can be useful to solve stochastic models arising in the performance evaluation of telecommunications and computer systems. We contribute to this technique in this paper by extending our recently developed variant of the Laguerre method for numerically inverting Laplace transforms to multidimensional Laplace transforms. An important application of multidimensional inversion is to calculate time-dependent performance measures of stochastic systems. Key features of our new algorithm are: (1) an efficient FFT-based extension of our previously developed variant of the Fourierseries method to calculate the coefficients of the multidimensional Laguerre generating function, and (2) systematic methods for scaling to accelerate convergence of infinite series, using Wynn's ε-algorithm and exploiting geometric decay rates of Laguerre coefficients. These features greatly speed up the algorithm while controlling errors. We illustrate the effectiveness of our algorithm through numerical examples. For many problems, hundreds of function evaluations can be computed in just a few seconds.     

Accurate determination of the frequency-to-time-domain matrix and its application to the inverse laplace transform of high order systems

A technique for accurately determining the inverse of the frequency to time domain matrix is developed. The matrix is applied to the inverse Laplace transformation evaluation.     

Hybrid laplace transform/weighting function scheme for transient multidimensional conservation equations

A hybrid Laplace transform/weighting function scheme is developed for solving time-dependent multidimensional conservation equations. The new method removes the time derivatives from the governing differential equations using the Laplace transform and solves the associated equation with the weighting function scheme. The similarity transform method is used to treat the complex coefficient system of the equations, which allows the simplest form of complex number functions to be obtained, and then to use the partial fractions method or a numerical method to invert the Laplace transform and transform the functions to the physical plane. Three different examples have been analyzed by the present method. The present method solutions are compared in tables with the exact solutions and those obtained by the other numerical methods. It is found that the present method is a reliable and efficient numerical tool.     

On the inverse Hough transform

In this paper, an inverse Hough transform algorithm is proposed. This algorithm reconstructs correctly the original image, using only the data of the Hough transform space and it is applicable to any binary image. As a first application, the inverse Hough transform algorithm is used for straight-line detection and filtering. The lines are detected not just as continuous straight lines, which is the case of the standard Hough transform, but as they really appear in the original image, i.e., pixel by pixel. To avoid the quantization effects in the Hough transform space, inversion conditions are defined, which are associated only with the dimensions of the images. Experimental results indicate that the inverse Hough transform algorithm is robust and accurate     

Laplace transform inversions using optimal contours in the complex plane

A numerical method for computing inverse Laplace transforms is proposed. In this method, the complex contour integral defining the inverse transform is computed over an equivalent contour as proposed by Talbot and Evans. Special contours, called optimal contours, are constructed so that the transformed real integrand decreases exponentially to zero as z runs along such a contour to infinity. The efficient Clenshaw-Curtis quadrature is employed for the final evaluation. The presented method is competitive and compares favourably with those of Talbot and Evans.     

基于高通滤波的多光谱图像融合方法*

提出了一种基于高通滤波的多光谱图像与高空间分辨率图像融合的方法.该算法首先对高空间分辨率图像进行高通滤波,然后将滤波后的图像与HIS正变换后的强度分量进行融合处理,再进行HIS 逆变换,得到最后的融合图像.通过将小波方法与HIS变换法的融合结果进行对比评价,表明了该方法在提高多光谱图像的空间细节表现能力和保持光谱信息上都有很好的效果.