Mathematics Commons^™

Sparse Equation-Eigen Solvers For Symmetric/Unsymmetric Positive-Negative-Indefinite Matrices With Finite Element And Linear Programming Applications, Hakakizumwami Birali Runesha

Civil & Environmental Engineering Theses & Dissertations

Vectorized sparse solvers for direct solutions of positive-negative-indefinite symmetric systems of linear equations and eigen-equations are developed. Sparse storage schemes, re-ordering, symbolic factorization and numerical factorization algorithms are discussed. Loop unrolling techniques are also incorporated in the coding to enhance the vector speed. In the indefinite solver, which employs various pivoting strategies, a simple rotation matrix is introduced to simplify the computer implementation. Efficient usage of the incore memory is accomplished by the proposed "restart memory management" schemes. A sparse version of the Interior Point Method, IPM, has also been implemented that incorporates the developed indefinite sparse solver for linear …