Peer Methods for the Solution of Large-Scale Differential Matrix Equations

We consider the application of implicit and linearly implicit (Rosenbrock-type) peer methods to matrix-valued ordinary differential equations. In particular the differential Riccati equation (DRE) is investigated. For the Rosenbrock-type schemes, a reformulation capable of avoiding a number of Jacobian applications is developed that, in the autonomous case, reduces the computational complexity of the algorithms. Dealing with large-scale problems, an efficient implementation based on low-rank symmetric indefinite factorizations is presented. The performance of both peer approaches up to order 4 is compared to existing implicit time integration schemes for matrix-valued differential equations.Comment: 29 pages, 2 figures (including 6 subfigures each), 3 tables, Corrected typo

Mergers Among German Cooperative Banks. A Panel-based Stochastic Frontier Analysis

Based on an unbalanced panel of all Bavarian cooperative banks for the years of 1989-97 which includes information on 283 mergers, we analyze motives and cost effects of small-scale mergers in German banking. Estimating a frontier cost function with a time-variable stochastic efficiency term we show that positive scale and scope effects from a merger arise only if the merged unit closes part of the former branch network. When we compare actual mergers to a simulation of hypothetical mergers, size effects of observed mergers turn out to be slightly more favorable than for all possible mergers. Banks taken over by others are less efficient than the average bank in the same size class, but exhibit on average the same efficiency as the acquiring firms. For the post-merger phase, our empirical results provide no evidence for efficiency gains from merging, but point instead to a leveling off of differences among the merging units.banking, mergers, efficiency, stochastic frontier

Methods of calculating ionization energies of multielectron (five or more) isoelectronic atomic ions

We have previously used simple empirical equations to reproduce the literature values of the ionization energies of isoelectronic sequences of up to four electrons which gave very good agreement. We reproduce here a kinetic energy expression with corrections for relativity and Lamb shift effects which give excellent agreement with the literature values. These equations become more complex as the number of electrons in the system increases. Alternative simple quadratic expressions for calculating ionization energies of multielectron ions are discussed. A set of coefficients when substituted into a simple expression produces very good agreement with the literature values. Our work shows that Slater's rules are not appropriate for predicting trends or screening constants. This work provides very strong evidence that ionization energies are not functions of complete squares, and when calculating ionization energies electron transition/relaxation has to be taken into account. We demonstrate clearly that for particular isoelectronic sequences, the ionizing electrons may occupy different orbitals and in such cases more than one set of constants are needed to calculate the ionization energies

The Loss in Efficiency from Using Grouped Data

We derive the efficiency loss from using grouped data to estimate coefficients of variables that vary across groups but not individuals within a group (e.g., state unemployment rates) when micro data are unavailable on the dependent variable. We present an empirical example of our theoretical results, and show that the efficiency loss in this application is small.grouped data, relative efficiency