Research Article
On Solving Pentadiagonal Linear Systems via Transformations
Algorithm 4
Second symbolic algorithm for solving pentadiagonal linear system.
To find the solution of PLS (1) using the transformed system (14), we proceed as follows: | INPUT Order of the matrix and the components , , . | OUTPUT The solution vector . | Step 1. Use DETGPENTA algorithm [14] or DETGPENTA algorithm [16] to check the non-singularity of the coefficient matrix | of the system (1). | Step 2. If , then Exit and Print Message (“No solutions”) end if. | Step 3. Set . If then end if. | Step 4. , , and . | Step 5. Set . If then end if. | Step 6. , , and . | Step 7. For do | Compute and simplify: | , | , | If then end if. | , | , | , | End do. | , | . If then end if. | , | , | . If then end if. | , | , | Step 8. Compute the solution vector using , . | For do | Compute and simplify: | | End do. | Step 9. Substitute in all expressions of the solution vector . |
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