A Method for Solving Cyclic Block Penta-diagonal Systems of Linear Equations
This provides a direct method for solving a specific class of linear systems, which is incremental for researchers working on numerical linear algebra.
The authors generalize a method for solving cyclic block three-diagonal systems to handle cyclic block penta-diagonal systems by introducing two new variables, splitting the system into three block pentagonal systems solvable by known direct methods. Numerical examples demonstrate the algorithm's implementation.
A method for solving cyclic block three-diagonal systems of equations is generalized for solving a block cyclic penta-diagonal system of equations. Introducing a special form of two new variables the original system is split into three block pentagonal systems, which can be solved by the known methods. As such method belongs to class of direct methods without pivoting. Implementation of the algorithm is discussed in some details and the numerical examples are present.