### Refine

#### Year of publication

- 1996 (23) (remove)

#### Document Type

- Report (23) (remove)

#### Faculty / Organisational entity

The paper deals with parallel-machine and open-shop scheduling problems with preemptions and arbitrary nondecreasing objective function. An approach to describe
the solution region for these problems and to reduce them to minimization problems on polytopes is proposed. Properties of the solution regions for certain problems are investigated. lt is proved that open-shop problems with unit processing times are equivalent to certain parallel-machine problems, where preemption is allowed at arbitrary time. A polynomial algorithm is presented transforming a schedule of one type into a schedule of the other type.

This document offers a concise introduction to the Goal Question Metric Paradigm (GQM Paradigm), and surveys research on applying and extending the GQM Paradigm. We describe the GQM Paradigm in terms of its basic principles, techniques for structuring GQM-related documents, and methods for performing tasks of planning and implementing a measurement program based on GQM. We also survey prototype software tools that support applying the GQM Paradigm in various ways. An annotated bibliography lists sources that document experience gained while using the GQM Paradigm and offer in-depth information about the GQM Paradigm.

In der industriellen Praxis werden immer häufiger Verbesserungs- und Meßansätze zur Steigerung der Qualität von Software-Produkten und -Projektdurchführungen diskutiert. Dieser Artikel gibt eine Übersicht über potentielle Ansätze zur kontinuierliche Software-Qualitätsverbesserung:
QIP, CMM und AMI. Aus dem Vergleich der Verbesserungsansätze geht hervor, daß u.a. zielorientiertes Messen eine integrale Technologie zur Verbesserung ist. Deshalb wird in diesem Artikel ein Ansatz für zielorientiertes Messen, der GQM-Ansatz, detaillierter diskutiert. Insbesondere wird auf die Anwendung in der Praxis eingegangen, wobei die Erfahrungen aus realen Projekten in Form von Richtlinien vorgestellt werden. Der Artikel will Praktikern einen Einstieg in die Software Qualitätsverbesserung mittels Messen vermittlen.

In recent years, Smolyak quadrature rules (also called hyperbolic cross points or sparse grids) have gained interest as a possible competitor to number theoretic quadratures for high dimensional problems. A standard way of comparing the quality of multivariate quadrature formulas
consists in computing their \(L_2\)-discrepancy. Especially for larger dimensions, such computations are a highly complex task. In this paper we develop a fast recursive algorithm for computing the \(L_2\)-discrepancy (and related quality measures) of general Smolyak quadratures. We carry out numerical comparisons between the discrepancies of certain Smolyak rules, Hammersley and Monte Carlo sequences.

A notion of discrepancy is introduced, which represents the integration error on spaces of \(r\)-smooth periodic functions. It generalizes the diaphony and constitutes a periodic counterpart to the classical \(L_2\)-discrepancy as weil as \(r\)-smooth versions of it introduced recently by Paskov [Pas93]. Based on previous work [FH96], we develop an efficient algorithm for computing periodic discrepancies for quadrature formulas possessing certain tensor product structures, in particular, for Smolyak quadrature rules (also called sparse grid methods). Furthermore, fast algorithms of computing periodic discrepancies for lattice rules can easily be derived from well-known properties of lattices. On this basis we carry out numerical comparisons of discrepancies between Smolyak and lattice rules.

This paper investigates the convergence of the Lanczos method for computing the smallest eigenpair of a selfadjoint elliptic differential operator via inverse iteration (without shifts).
Superlinear convergence rates are established, and their sharpness is investigated for a simple model problem. These results are illustrated numerically for a more difficult problem.

The first part of this paper studies a Levenberg-Marquardt scheme for nonlinear inverse problems where the corresponding Lagrange (or regularization) parameter is chosen from an inexact Newton strategy. While the convergence analysis of standard implementations based on trust region strategies always requires the invertibility of the Fréchet derivative of the nonlinear operator at the exact solution, the new Levenberg-Marquardt scheme is suitable for ill-posed problems as long as the Taylor remainder is of second order in the interpolating metric between the range and dornain
topologies. Estimates of this type are established in the second part of the paper for ill-posed parameter identification problems arising in inverse groundwater hydrology. Both, transient and steady state data are investigated. Finally, the numerical performance of the new Levenberg-Marquardt scheme is
studied and compared to a usual implementation on a realistic but synthetic 2D model problem from the engineering literature.

This paper develops truncated Newton methods as an appropriate tool for nonlinear inverse problems which are ill-posed in the sense of Hadamard. In each Newton step an approximate solution for the linearized problem is computed with the conjugate gradient method as an inner iteration. The conjugate gradient iteration is terminated when the residual has been reduced to a prescribed percentage. Under certain assumptions on the nonlinear operator it is shown that the algorithm converges and is stable if the discrepancy principle is used to terminate the outer iteration.
These assumptions are fulfilled , e.g., for the inverse problem of identifying the diffusion coefficient in a parabolic differential equation from distributed data.

A convergence rate is established for nonstationary iterated Tikhonov regularization, applied to ill-posed problems involving closed, densely defined linear operators, under general conditions on the iteration parameters. lt is also shown that an order-optimal accuracy is attained when a certain a posteriori stopping rule is used to determine the iteration number.

Quasi-Monte Carlo Radiosity
(1996)

The problem of global illumination in computer graphics is described by a second kind Fredholm integral equation. Due to the complexity of this equation, Monte Carlo methods provide an interesting tool for approximating
solutions to this transport equation. For the case of the radiosity equation, we present the deterministic method of quasi-rondom walks. This method very efficiently uses low discrepancy sequences for integrating the Neumann series and consistently outperforms stochastic techniques. The method of quasi-random walks also is applicable to transport problems in settings other
than computer graphics.

The calculation of form factors is an important problem in computing the global illumination in the radiosity setting. Closed form solutions often are only available for objects without obstruction and are very hard to calculate. Using Monte Carlo integration and ray tracing provides a fast and elegant tool for the estimation of the form factors. In this paper we show, that using deterministic low discrepancy sample points is superior to random sampling, resulting in an acceleration of more than half an order of magnitude.

Let \(a_1,\dots,a_n\) be independent random points in \(\mathbb{R}^d\) spherically symmetrically but not necessarily identically distributed. Let \(X\) be the random polytope generated as the convex hull of \(a_1,\dots,a_n\) and for any \(k\)-dimensional subspace \(L\subseteq \mathbb{R}^d\) let \(Vol_L(X) :=\lambda_k(L\cap X)\) be the volume of \(X\cap L\) with respect to the \(k\)-dimensional Lebesgue measure \(\lambda_k, k=1,\dots,d\). Furthermore, let \(F^{(i)}\)(t):= \(\bf{Pr}\) \(\)(\(\Vert a_i \|_2\leq t\)),
\(t \in \mathbb{R}^+_0\) , be the radial distribution function of \(a_i\). We prove that the expectation
functional \(\Phi_L\)(\(F^{(1)}, F^{(2)},\dots, F^{(n)})\) := \(E(Vol_L(X)\)) is strictly decreasing in
each argument, i.e. if \(F^{(i)}(t) \le G^{(i)}(t)t\), \(t \in {R}^+_0\), but \(F^{(i)} \not\equiv G^{(i)}\), we show \(\Phi\) \((\dots, F^{(i)}, \dots\)) > \(\Phi(\dots,G^{(i)},\dots\)). The proof is clone in the more general framework
of continuous and \(f\)- additive polytope functionals.

Let \(a_1,\dots,a_m\) be independent random points in \(\mathbb{R}^n\) that are independent and identically distributed spherically symmetrical in \(\mathbb{R}^n\). Moreover, let \(X\) be the random polytope generated as the convex hull of \(a_1,\dots,a_m\) and let \(L_k\) be an arbitrary \(k\)-dimensional
subspace of \(\mathbb{R}^n\) with \(2\le k\le n-1\). Let \(X_k\) be the orthogonal projection image of \(X\) in \(L_k\). We call those vertices of \(X\), whose projection images in \(L_k\) are vertices of \(X_k\)as well shadow vertices of \(X\) with respect to the subspace \(L_k\) . We derive a distribution independent sharp upper bound for the expected number of shadow vertices of \(X\) in \(L_k\).

Software development organizations measure their real-world processes, products, and resources to achieve the goal of improving their practices. Accurate and useful measurement relies on explicit models of the real-world processes, products, and resources. These explicit models assist with planning measurement, interpreting data, and assisting developers with their work. However, little work has been done on the joint use of measurem(int and process technologies. We hypothesize that it is possible to integrate measurement and process technologies in a way that supports automation of measurement-based feedback. Automated support for measurementbased feedback means that software developers and maintainers are provided with on-line, detailed information about their work. This type of automated support is expected to help software professionals gain intellectual control over their software projects. The dissertation offers three major contributions. First, an integrated measurement and
process modeling framework was constructed. This framework establishes the necessary foundation for integrating measurement and process technologies in a way that will permit automation. Second, a process-centered software engineering environment was developed to support measurement-based feedback. This system provides personnel with information about the tasks expected of them based on an integrated set of measurement and process views. Third, a set of assumptions and requirements about that system were examined in a controlled experiment. The experiment compared the use of different levels of automation to evaluate the acceptance and effectiveness of measurement-based feedback.

It is shown that Tikhonov regularization for ill- posed operator equation
\(Kx = y\) using a possibly unbounded regularizing operator \(L\) yields an orderoptimal algorithm with respect to certain stability set when the regularization parameter is chosen according to the Morozov's discrepancy principle. A more realistic error estimate is derived when the operators \(K\) and \(L\) are related to a Hilbert scale in a suitable manner. The result includes known error estimates for ordininary Tikhonov regularization and also the estimates available under the Hilbert scale approach.

Skelettbasierte implizite Flächen haben aufgrund ihrer Fähigkeit, durch automatisches Verschmelzen aus wenigen, einfachen Primitiven komplexe Strukturen zu formen, für Modellierung, Visualisierung und Animation zunehmend an Bedeutung gewonnen. Eine wesentliche Schwierigkeit beim Einsatz impliziter Flächen ist nach wie vor eine effiziente Visualisierung der resultierenden Objekte. In der vorliegenden
Arbeit werden die grundlegenden Ideen einer Methode zur partikelgestützten Triangulierung skelettbasierter impliziter Flächen beschrieben, die die Vorteile einer partikelgestützten Abtastung
impliziter Flächen mit der polygonalen Darstellung durch Dreiecke kombiniert. Der Algorithmus ist in der Lage, effizient auf dynamische Veränderungen der Gestalt sowie das Auseinanderreißen nicht allzu
komplexer implizit gegebener Objekte zu reagieren. Zusätzlich besteht die Möglichkeit, die Triangulierung krümmungsadaptiv zu gestalten, um bei gleichbleibender Darstellungsqualität eine Reduktion der Dreiecksanzahl zu erreichen.