The null space problem I. complexity
SIAM Journal on Algebraic and Discrete Methods
Computing a sparse basis for the null space
SIAM Journal on Algebraic and Discrete Methods
ABS projection algorithms: mathematical techniques for linear and nonlinear equations
ABS projection algorithms: mathematical techniques for linear and nonlinear equations
The null space problem II. Algorithms
SIAM Journal on Algebraic and Discrete Methods
Substructuring methods for computing the Nullspace of equilibrium matrices
SIAM Journal on Matrix Analysis and Applications
Nested dissection for sparse nullspace bases
SIAM Journal on Matrix Analysis and Applications
Sparse QR factorization in MATLAB
ACM Transactions on Mathematical Software (TOMS)
A primal null-space affine-scaling method
ACM Transactions on Mathematical Software (TOMS)
Multifrontal Computation with the Orthogonal Factors of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Hi-index | 0.00 |
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.