Ziyang Wang

The matrix sign function has a key role in several applications in numerical linear algebra. This paper presents a novel iterative approach with a sixth order of convergence to efficiently compute this function. The scheme is constructed via the employment of a nonlinear equations solver for simple roots. Then, the convergence of the extended matrix procedure is investigated to demonstrate the sixth rate of convergence. Basins of attractions for the proposed solver are given to show its global convergence behavior as well. Finally, the numerical experiments demonstrate the effectiveness of our approach compared to classical methods.

The Heston-Hull-White (HHW) model is a generalization of the classical Heston approach that incorporates stochastic interest rates, making it a more accurate representation of financial markets. In this work, we investigate a computational procedure via a three-dimensional partial differential equation (PDE) to solve option pricing problems under the HHW framework. We propose a local radial basis function–finite difference (RBF–FD) framework under the integration of a new variant of the multiquadric function for efficiently resolving the model. Our study highlights the error analysis of the proposed weights for the first and second derivatives of a suitable function and demonstrates the effectiveness of the RBF–FD approach for this high-dimensional financial model.