THEORETICAL BASIS AND PRACTICAL APPLICATION OF THE SEIDEL METHOD : ITERATIVE APPROACH TO SOLVING LINEAR SYSTEMS
Keywords:
Zeydel method , iterative method , linear algebra, approximation condition , simple iteration , matrices , eigenvalues numbers , solution accuracy , system solution , theorem proofAbstract
In the article Seidel method , that is linear one step first orderly iterative of themethod essence , application and approach conditions surrounding illuminated . Seidel method simple iteration from the method different aspects , in particular , iteration in
the process initial from rapprochements come out consecutively calculation scheme The method is explained . approach condition theorem in the form of brought , its proof matrices and their typical numbers based on done increased . Seidel method approach
for matrix typical by the modulus of numbers suddenly small to be necessity It is also emphasized that simple iteration method with in comparison Seidel method advantages and disadvantages , conditions compliance when done faster approach theorem and
examples through is based on . Article in the end practical example brought , Seidel 5 rooms of the method in accuracy solution find process table in the form of shown . This article linear algebra and iterative methods in the field research take visitors for important source become service does .
References
1.
Golub, G. H., & Van Loan, C. F. (2013). Matrix Computations (4th ed.). Johns
Hopkins University Press.
2.
Saad, Y. (2003). Iterative Methods for Sparse Linear Systems (2nd ed.). SIAM.
3.
4.
Demmel, J. W. (1997). Applied Numerical Linear Algebra. SIAM.
Varga, R. S. (2000). Matrix Iterative Analysis (2nd ed.). Springer.
