Hyung-Myung Kim Korea Advanced Institute of Science and Technology (KAIST) Department of Electrical Engineering 373-1 Kusong-Dong, Yusong-Gu Taejon 305-701 South Korea Abstract. The authors derive an adaptive version of cubic convolution interpolation for the enlargement or reduction of digital images by arbitrary scaling factors. The adaptation is performed in each subblock (typically L3L rect...

We introduce a solver for stiff ordinary differential equations (ODEs) that is based on the deferred correction scheme for the corresponding Picard integral equation. Our solver relies on the assumption that the solution can be accurately represented by a combination of carefully selected complex exponentials. The solver’s accuracy and stability rely on the computation of highly accurate quadra...

Since there is no analytic solution for arithmetic average options until present, developing an efficient numerical algorithm becomes a promising alternative. One of the most famous numerical algorithms is introduced by Hull and White (J Deriv 1:21–31, 1993). Motivated by the common idea of reducing the nonlinearity error in the adaptive mesh model in Figlewski and Gao (J Financ Econ 53:313–351...

Generation of meshes adapted to a given function u requires a specially designed metric. For metric derived from the Hessian of u, optimal error estimates for the interpolation error on simplicial meshes have been proved in [2, 5, 8, 10, 11]. The Hessian-based metric has been successfully applied to adaptive solution of PDEs [4, 7, 9]. However, theoretical estimates have required to make an add...