The time complexity for testing whether an n-by-n real matrix is a P-matrix is reduced from O(2n n 3) to O(2 n ) by applying recursively a criterion for P-matrices based on Schur complementation. A Matlab program implementing the... more
The time complexity for testing whether an n-by-n real matrix is a P-matrix is reduced from O(2n n 3) to O(2 n ) by applying recursively a criterion for P-matrices based on Schur complementation. A Matlab program implementing the associated algorithm is provided.
A brief but concise review of methods to generate P-matrices (i.e., matrices having positive principal minors) is provided and motivated by open problems on P-matrices and the desire to develop and test efficient methods for the detection... more
A brief but concise review of methods to generate P-matrices (i.e., matrices having positive principal minors) is provided and motivated by open problems on P-matrices and the desire to develop and test efficient methods for the detection of P-matrices. Also discussed are operations that leave the class of P-matrices invariant. Some new results and extensions of results regarding P-matrices are included.
Sparse Matrix Methods in Optimization. [SIAM Journal on Scientific and Statistical Computing 5, 562 (1984)]. Philip E. Gill, Walter Murray, Michael A. Saunders, Margaret H. Wright. Abstract. Optimization algorithms typically require ...
We develop a data-sparse and accurate approximation of the normalised hyperbolic operator sine family generated by a strongly P-positive elliptic operator defined in (4, 7). In the preceding papers (14)-(18), a class of H-matrices has... more
We develop a data-sparse and accurate approximation of the normalised hyperbolic operator sine family generated by a strongly P-positive elliptic operator defined in (4, 7). In the preceding papers (14)-(18), a class of H-matrices has been analysed which are data-sparse and allow an approximate matrix arithmetic with almost linear complexity. An H-matrix approximation to the operator exponent with a strongly
A 3-D domain decomposition method for fully coupled electrothermomechanical contact problems is presented. The formulation is based on the cell method. Contacting domains are linked together by introducing a new reference frame (i.e., the... more
A 3-D domain decomposition method for fully coupled electrothermomechanical contact problems is presented. The formulation is based on the cell method. Contacting domains are linked together by introducing a new reference frame (i.e., the mortar surface). Field discontinuities across contact interfaces are simulated by suitable constitutive operators. It is shown that the same coupling strategy can be adopted for the electrical, thermal, and mechanical contact problems. Compatibility constraints are imposed by means of dual Lagrange multipliers defined on the mortar surface. Coupled nonlinear algebraic equations are finally cast into a saddle-point problem, which is resolved by combining the Schur complement method with the Newton-Raphson method. The proposed mortar approach is validated with a commercial 3-D finite-element method multiphysics software package.
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A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution... more
A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution of which is crucial. A new factorization of the Schur complement for such a system is proposed and its characteristics discussed. The factorization introduces two complex factors that are complex conjugate to each other. The proposed solution methodology involves the application of a parallel linear domain decomposition solver---FETI-DPH---for the solution of the subproblems with the complex factors. Numerical properties of FETI-DPH in this context are demonstrated, including numerical and parallel scalability and regularization dependence. The new factorization can be used to solve Schur complement systems arising in both range-space and full-space formulations. In both cases, numerical results indicate that the complex factorization is promising.
Parallel implicit iterative solution techniques are considered for application to a compressible hypersonic Navier-Stokes solver on unstructured meshes. The construction of parallel preconditioners with quasi-optimal convergence... more
Parallel implicit iterative solution techniques are considered for application to a compressible hypersonic Navier-Stokes solver on unstructured meshes. The construction of parallel preconditioners with quasi-optimal convergence properties with respect to their serial counterpart is a key issue in the design of modern parallel implicit schemes. Two types of non-overlapping preconditioners are presented and compared. The first one is an additive
