http://hdl.handle.net/1813/5440 http://dspace.library.cornell.edu/retrieve/31734 http://hdl.handle.net/1813/5440 Search the Channel search http://dspace.library.cornell.edu/simple-search http://hdl.handle.net/1813/5598 Title: Accurate Solution of Weighted Least Squares by Iterative Methods <br/> <br/>Authors: Bobrovnikova, Elena Y.; Vavasis, Stephen A. <br/> <br/>Abstract: We consider the weighted least-squares (WLS) problem with a very ill-conditioned weight matrix. Weighted least-squares problems arise in many applications including linear programming, electrical networks, boundary value problems, and structures. Because of roundoff errors, standard iterative methods for solving a WLS problem with ill-conditioned weights may not give the correct answer. Indeed, the difference between the true and computed solution (forward error) may be large. We propose an iterative algorithm, called MINRES-L, for solving WLS problems. The MINRES-L method is the application of MINRES, a Krylov-space method due to Paige and Saunders, to a certain layered linear system. Using a simplified model of the effects of round off error, we prove that MINRES-L gives answers with small forward error. We present computational experiments for some applications. http://hdl.handle.net/1813/5597 Title: Local correlation energies of two-electron atoms and model systems <br/> <br/>Authors: Huang, Chien-Jung; Umrigar, C.J. <br/> <br/>Abstract: We present nearly-local definitions of the correlation energy density, and its potential and kinetic components, and evaluate them for several two-electron systems. This information should provide valuable guidance in constructing better correlation functionals than those in common use. In addition, we demonstrate that the quantum chemistry and the density functional definitions of the correlation energy rapidly approach one another with increasing atomic number. http://hdl.handle.net/1813/5596 Title: Quality Mesh Generation in Higher Dimensions <br/> <br/>Authors: Mitchell, Scott A.; Vavasis, Stephen A. <br/> <br/>Abstract: We consider the problem of triangulating a d-dimensional region. Our mesh generation algorithm, called QMG, is a qradtree-based algorithm that can triangulate any polyhedral region including nonconvexregions with holes. Furthermore, our algorithm guarantees a bounded aspect ratio triangulation provided that the input domain itself has no sharp angles. Finally, our algorithm is guaranteed never to over refine the domain in the sense that the number of simplices produced by QMG is bounded above by a factor times the number produced by any competing algorithm, where the factor depends on the aspect ratio bound satisfied by the competing algorithm. The QMG algorithm has been implemented in C++ and is used as a mesh generator for the finite element method. http://hdl.handle.net/1813/5595 Title: Model fermion Monte Carlo with correlated pairs II <br/> <br/>Authors: Kalos, M.H.; Schmidt, K.E. <br/> <br/>Abstract: Correlated dynamics can produce stable algorithms for excited states of quantum many-body problems. We study a variety of harmonic oscillator problems to demonstrate the kinds of correlations needed. We show that marginally correct dynamics that produce a stable overlap with an antisymmetrictrial function give the correct fermion ground state.