To find the solution of PLS (1) using the transformed system (8), 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 , , , and . | Step 4. Set , , , , and . | Step 5. For do | Compute and simplify: | , | , | , | , | , | End do. | , | , | , | , | , | , | , | Step 6. Compute the solution vector using , . | For do | Compute and simplify: | | End do. |
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