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The paper presents the discussion on extension of potential application of the Choleski-Banachiewicz algorithm to the system of linear equations with non-positive definite matrices. It is shown that the method is also stable in case of systems with negative definite matrices and sometimes may be also successful if the matrix is neither positive nor negative definite. The algorithm handles systems with complex symmetric (not Hermitian) matrices, too. This fact has deep physical sense and engineering applications since systems with negative definite matrices are common in tasks of dynamics and post buckling analysis in civil and mechanical engineering. Possibility of utilization of Choleski-Banachiewicz algorithm to such problems can be very practical. The entire analysis has been carried out within Mathematica ® environment.

Choleski-Banachiewicz Approach to Systems with Non-positive Definite Matrices with Mathematica ®