Convergence of Preconditioned Gauss-Seidel Iterative Method For Matrices
Keywords:
Gauss-Seidel iterative method, Preconditioning, L--matrix, Splitting, Nonnegative matrixAbstract
A great many real-life situations are often modeled as linear system of equations, . Direct methods of solution of such systems are not always realistic, especially where the coefficient matrix is very large and sparse, hence the recourse to iterative solution methods. The Gauss-Seidel, a basic iterative method for linear systems, is one such method. Although convergence is rarely guaranteed for all cases, it is established that the method converges for some situations depending on properties of the entries of the coefficient matrix and, by implication, on the algebraic structure of the method. However, as with all basic iterative methods, when it does converge, convergence could be slow. In this research, a preconditioned version of the Gauss-Seidel method is proposed in order to improve upon its convergence and robustness. For this purpose, convergence theorems are advanced and established. Numerical experiments are undertaken to validate results of the proved theorems
Downloads
Published
Issue
Section
Similar Articles
- Gulumbe S. Usman, Umar Usman, Aremu Kazeem Olalekan, Odeyale, Abideen Babatunde , The Generalized Odd Generalized Exponential Gompertz Distribution with Applications , Communication In Physical Sciences: Vol. 10 No. 1 (2023): VOLUME 10 ISSUE 1
- Nwanya, Julius Chigozie, Njoku, Kevin Ndubuisi Chikezie, A New Approach to Solving Transportation Problems: The Middle Cell Method , Communication In Physical Sciences: Vol. 10 No. 3 (2023): VOLUME 10 ISSUE 3
- I. Usman, Modification of White Method for Quantitative Evaluation of 5hydroxymethylfurfural in Honey , Communication In Physical Sciences: Vol. 5 No. 1 (2020): VOLUME 5 ISSUE 1
- Muhammad Bello, Musa Bello, Dunah Lawissense Godfrey, Effect of Multimedia-Enriched Lecture Method on Retention Among Secondary School Physics Students in Kano Metropolis, Nigeria , Communication In Physical Sciences: Vol. 12 No. 3 (2025): VOLUME 12 ISSUE 3
- Martins Moses, John Stanley, Adam Aliyu, Benjamin Biko, Synthesis and Characterization of Graphene Oxide Nanoparticles Using Graphite Dust , Communication In Physical Sciences: Vol. 9 No. 4 (2023): VOLUME 9 ISSUE 4
- O. V. Ikpeazu, Ifeanyi E. Otuokere,, K. K. Igwe, Colorimetric Determination of Stability Constant of Acetaminophen-Cu(II) complex by Classical Equation Depending on Stoichiometric Curves , Communication In Physical Sciences: Vol. 5 No. 3 (2020): VOLUME 5 ISSUE 3
- Njoku, Kevin Ndubuisi Chikezie, Okoli, Odilichukwu Christian., A Note On The Proofs Of Cramer’s Formula , Communication In Physical Sciences: Vol. 11 No. 1 (2024): VOLUME 11 ISSUE 1
- Chigozie. Chibuisi, Bright O. Osu, Kevin Ndubuisi C. Njoku, Chukwuka Fernando Chikwe, A Mathematical Investigation of Fuel Subsidy Removal and its Effects on Nigerian Economy , Communication In Physical Sciences: Vol. 11 No. 3 (2024): VOLUME 11 ISSUE 3
- Samson Osinachi Nwadibia, Henry Patrick Obong, Ephraim Okechukwu Chukwuocha, Analytical Solutions of the Schrodinger Equation with q-Deformed Modified Mobius Square Potential Using the Nikiforov-Uvarov Method , Communication In Physical Sciences: Vol. 9 No. 4 (2023): VOLUME 9 ISSUE 4
- Akaezue Nelson Nwagbogwu, Ngiangia Alalibor Thompson, Onyeaju Michael Chukwudi, Thermal Properties of Diffusing Species into Some Host Metals , Communication In Physical Sciences: Vol. 11 No. 4 (2024): VOLUME 11 ISSUE 4
You may also start an advanced similarity search for this article.