• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.3
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• pp.243-291
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• 2020

In this paper, multi-block generalized backward differentiation methods for numerical solutions of ordinary differential and differential algebraic equations are introduced. This class of linear multi-block methods is implemented as multi-block boundary value methods (MB₂ VMs). The root distribution of the stability polynomial of the new class of methods are determined using the Wiener-Hopf factorization of a matrix polynomial for the purpose of their correct implementation. Numerical tests, showing the potential of such methods for output of multi-block of solutions of the ordinary differential equations in the new approach are also reported herein. The methods which output multi-block of solutions of the ordinary differential equations on application, are unlike the conventional linear multistep methods which output a solution at a point or the conventional boundary value methods and multi-block methods which output only a block of solutions per step. The MB₂ VMs introduced herein is a novel approach at developing very large scale integration methods (VLSIM) in the numerical solution of differential equations.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.1117-1120
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• 1999

The main purpose of padding methods is to extend the boundary segments of arbitrarily shaped objects to a regular grid so that the common block based coding technique, such as 8${\times}$8 DCT, can be applied. In the conventional padding methods used in MPEG-4: LPE and zero padding, the main process is based on 8${\times}$8 blocks. On the contrary, we propose a new padding method based on pixel-by-pixel. The proposed method puts pixels into a multi-busier using the typical value of each boundary blocks and reproduces new boundary blocks. Simulation results show that the proposed method reduces the conventional padding method and improves the coding efficiency of the conventional padding method.