In this paper, we contribute higher order operator-splitting method improved by Zassenhaus product. We apply the contribution to classical and iterative splitting methods. The underlying analysis to obtain higher order operator-splitting methods is presented. While applying the methods to partial differential equations, the benefits of balancing time and spatial scales are discussed to accelera...

We present an iterative method based on the Hermitian and skew-Hermitian splitting for solving the continuous Sylvester equation. By using the Hermitian and skew-Hermitian splitting of the coefficient matrices A and B, we establish a method which is practically inner/outer iterations, by employing a CGNR-like method as inner iteration to approximate each outer iterate, while each outer iteratio...

Five numerical methods for pricing American put options under Heston’s stochastic volatility model are described and compared. The option prices are obtained as the solution of a two-dimensional parabolic partial differential inequality. A finite difference discretization on nonuniform grids leading to linear complementarity problems with M -matrices is proposed. The projected SOR, a projected ...

Timo Kaukoranta Olli Nevalainen University of Turku Turku Centre for Computer Science (TUCS) Department of Computer Science Lemminkäisenkatu 14 A FIN-20520 Turku, Finland Abstract. The well-known LBG algorithm uses binary splitting for generating an initial codebook, which is then iteratively improved by the generalized Lloyd algorithm (GLA). We study different variants of the splitting method ...

In this paper, efficient direct and iterative methods are described for solving a large random sparse non-symmetric linear system. Such systems of linear equations of huge order arise in several applications such as physics, mechanics, signal processing and other applications of real life problems. For this reason, we try to develop direct and iterative methods for solving such systems of linea...

We consider quadrature formulas of high order in time based on Radau–type, L–stable implicit Runge–Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs iterative deferred corrections to compute the solution at the collocation nodes of the quadrature formulas. The numerical stability is guaranteed by a dedic...

The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of ...

Thispaper presents a method of simultaneous localization and mapping (SLAM) in indoor environment using extended Kalman filter (EKF) with the straight line segments as the adopted geometrical feature. By using conventional two dimensional laser range finder (LRF) as the main sensor, robot finds a number of points scanned from the surrounding environment.Split-and-Merge is one of the mostpopular...