We propose a way to use the Markowitz pivot selection criterion for choosing the parameters of the extended ABS class of algorithms to present an effective algorithm for generating sparse null space bases. We explain in detail an efficient implementation of the algorithm, making use of the special MATLAB 7.0 functions for sparse matrix operations and the inherent efficiency of the ANSI C programming language. We then compare our proposed algorithm with an implementation of an efficient algorithm proposed by Coleman and Pothen with respect to the computing time and the accuracy and the sparsity of the generated null space bases. Our extensive numerical results, using coefficient matrices of linear programming problems from the NETLIB set of test problems show the competitiveness of our implemented algorithm.
