Implementation of a multi-reference double-excitation CI (MRD-CI) method is discussed and its results are compared with those of related techniques. This approach employs a configuration selection procedure to order the various generated species according to their energy-lowering capability and then uses an energy extrapolation procedure based on perturbation theory to obtain suitably accurate estimates of the eigenvalues of the entire MRD-CI space. By employing this selection procedure it is possible to test from 2000 to 4000 symmetry-adapted functions (SAF's) per second of CPU time on an IBM 370–168 system, thereby allowing one to apply the energy extrapolation quite conveniently to CI spaces consisting of several hundred thousand species. By systematically increasing the number of reference configurations in the MRD-CI it is clear that the limit of a full CI can be approached and as a result such a computational procedure appears to be generally valid for any type of electronic state and for any nuclea...

Applicability of the multi-reference double-excitation CI (MRD-CI) method to the calculation of electronic wavefunctions and comparison with related techniques

The authors' survey paper is devoted to the present state of computational methods in linear algebra. Questions discussed are the means and methods of estimating the quality of numerical solution of computational problems, the generalized inverse of a matrix, the solution of systems with rectangular and poorly conditioned matrices, the inverse eigenvalue problem, and more traditional questions such as algebraic eigenvalue problems and the solution of systems with a square matrix (by direct and iterative methods).

Computational methods of linear algebra

Combined use of proton-proton Overhauser enhancements and a distance geometry algorithm for determination of polypeptide conformations. Application to micelle-bound glucagon.

Im vorliegenden Beitrag werden Ansatze zur Berechnung des Gleichgewichtszustandes und damit zur Berechnung von Forin, Spannungen und Zuschnittsmasen vorgespannter Seilnetzkonstruktion untersucht. Durch eine Kombination von Methoden der Elastomechanik und der Ausgleichungsrechnung — die im Modell gemessenen Knotenpunktkoordinaten und Spannungen werden als zu verbessernde Beobachtungen aufgefast — kann die Gleichmaschigkeit im Innern des Netzes als Nebenbedingung berucksichtigt werden. Die Rechenansatze werden in solcher Weise hergeleitet, das sich gemeinsame Zuge verschiedener Iterationsverfahren zeigen. Als Nebenprodukt dieser Herleitung erhalt man die Aussage, das jeder Gleichgewichtszustand eines Netzes uber die Losung eines einzigen linearen Gleichungssystems mit positiv definiter und symmetrischer Koeffizientenmatrix erhalten werden kann. Damit kann man sich einen Uberblick verschaffen uber eine grose Anzahl von Gleichgewichtsfiguren, die zu einer bestimmten Anzahl von Festpunkten gehoren.

Einige Bemerkungen zur Berechnung von vorgespannten Seilnetzkonstruktionen

We present a unified and self-contained treatment of rational Krylov methods for approximating the product of a function of a linear operator with a vector With the help of general rational Krylov decompositions we reveal the connections between seemingly different approximation methods, such as the Rayleighâ��Ritz or shift-and-invert method, and derive new methods, for example a restarted rational Krylov method and a related method based on rational interpolation in prescribed nodes Various theorems known for polynomial Krylov spaces are generalized to the rational Krylov case Computational issues, such as the computation of so-called matrix Rayleigh quotients or parallel variants of rational Arnoldi algorithms, are discussed We also present novel estimates for the error arising from inexact linear system solves and the approximation error of the Rayleighâ��Ritz method Rational Krylov methods involve several parameters and we discuss their optimal choice by considering the underlying rational approximation problems In particular, we present different classes of optimal parameters and collect formulas for the associated convergence rates Often the parameters leading to best convergence rates are not optimal in terms of computation time required by the resulting rational Krylov method We explain this observation and present new approaches for computing parameters that are preferable for computations We give a heuristic explanation of superlinear convergence effects observed with the Rayleighâ��Ritz method, utilizing a new theory of the convergence of rational Ritz values All theoretical results are tested and illustrated by numerical examples Numerous links to the historical and recent literature are included

Rational Krylov Methods for Operator Functions

Numerische Methoden der linearen Algebra

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Numerische Methoden der linearen Algebra