New design of pivoted banded linear equation solver versus CLAPACK library routines

A new method of pivoting applicable to banded unsymmetric linear equation systems has been introduced. It limits the fill-in, preserves basic band structure and makes full use of allocated memory. Two new features of this method include multiple pivoting and the threshold factor use for pivoting decision. The stability or rather the solution precision has been investigated basing on the examples of classic ill conditioned equation system (Hilbert) and quasi-random system with still more difficult conditioning characteristic. Comprehensive test results have been presented in the easily readable graphic form. They prove the overall efficiency of new solvers and compare them favourably with the software from CLAPACK library.