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All Journal Bulletin of Electrical Engineering and Informatics Indonesian Journal of Electrical Engineering and Computer Science
Azali Saudi
Universiti Malaysia Sabah
Electrical & Electronics Engineering

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Modified iterative method with red-black ordering for image composition using poisson equation Zakariah Aris; Nordin Saad; A’qilah Ahmad Dahalan; Andang Sunarto; Azali Saudi
Bulletin of Electrical Engineering and Informatics Vol 10, No 4: August 2021
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/eei.v10i4.3076

Abstract

Image composition involves the process of embedding a selected region of the source image to the target image to produce a new desirable image seamlessly. This paper presents an image composition procedure based on numerical differentiation using the laplacian operator to obtain the solution of the poisson equation. The proposed method employs the red-black strategy to speed up the computation by using two acceleration parameters. The method is known as modified two-parameter over-relaxation (MTOR) and is an extension of the existing relaxation methods. The MTOR was extensively studied in solving various linear equations, but its usefulness in image processing was never explored. Several examples were tested to examine the effectiveness of the proposed method in solving the poisson equation for image composition. The results showed that the proposed MTOR performed faster than the existing methods.
Preconditioned successive over relaxation iterative method via semi-approximate approach for Burgers’ equation Nur Farah Azira Zainal; Jumat Sulaiman; Azali Saudi; Nur Afza Mat Ali
Indonesian Journal of Electrical Engineering and Computer Science Vol 29, No 3: March 2023
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v29.i3.pp1606-1613

Abstract

This paper proposes the combination of a preconditioner applied with successive over relaxation (SOR) iterative method for solving a sparse and huge scale linear system (LS) in which its coefficient matrix is a tridiagonal matrix. The purpose for applying the preconditioner is to enhance the convergence rate of SOR iterative method. Hence, in order to examine the feasibility of the proposed iterative method which is preconditioner SOR (PSOR) iterative method, first we need to derive the approximation equation of one-dimensional (1D) Burgers’ equation through the discretization process in which the second-order implicit finite difference (SIFD) scheme together with semi-approximate (SA) approach have been applied to the proposed problem. Then, the generated LS is modified into preconditioned linear system (PLS) to construct the formulation of PSOR iterative method. Furthemore, to analyze the feasibility of PSOR iterative method compared with other point iterative methods, three examples of 1D Burgers’ equation are considered. In conclusion, the PSOR iterative method is superior than PGS iterative method. The simulation results showed that our proposed iterative method has low iteration numbers and execution time.
Co-Authors Andang Sunarto A’qilah Ahmad Dahalan Jumat Sulaiman Nordin Saad Nur Afza Mat Ali Nur Farah Azira Zainal Zakariah Aris