Konrad Zuse und die ETH Zürich: Zum 100. Geburtstag des Informatikpioniers Konrad Zuse (22. Juni 2010)

Zusammenfassung: Der deutsche Bauingenieur Konrad Zuse (1910-1995) hat 1941 die Z3 vorgeführt, den ersten frei programmierbaren und in binärer Gleitpunktrechnung arbeitenden Rechner der Welt. Zudem entwickelte er mit seinem Plankalkül erste Ideen für eine allgemeine Programmiersprache. Vor 100 Jahren wurde der Informatikpionier in Berlin geboren. Als einzige Universität auf dem europäischen Festland hatte die ETH Zürich 1950 eine betriebsfähige programmgesteuerte Rechenmaschine, die gemietete Z4. Die Z4 ist eine Weiterentwicklung der im Krieg zerstörten Z3. Dank der mit diesem Gerät durchgeführten Forschungsarbeiten wurde das damalige von Eduard Stiefel geleitete Institut für angewandte Mathematik in kurzer Zeit weltberühmt. Der Verfasser dankt den Professoren Walter Gander, Martin Gutknecht und Carl August Zehnder für ihre tatkräftige Unterstützung, die um so wertvoller war, als die drei Pioniere der Gründerzeit, die Professoren Eduard Stiefel, Heinz Rutishauser und Ambros Speiser, gestorben sind und es nur noch wenige Zeitzeugen gib

From qd to LR, or, how were the qd and LR algorithms discovered?

Perhaps, the most astonishing idea in eigenvalue computation is Rutishauser's idea of applying the LR transform to a matrix for generating a sequence of similar matrices that become more and more triangular. The same idea is the foundation of the ubiquitous QR algorithm. It is well known that this idea originated in Rutishauser's qd algorithm, which precedes the LR algorithm and can be understood as applying LR to a tridiagonal matrix. But how did Rutishauser discover qd and when did he find the qd-LR connection? We checked some of the early sources and have come up with an explanatio

A Conversation with Peter Huber

Peter J. Huber was born on March 25, 1934, in Wohlen, a small town in the Swiss countryside. He obtained a diploma in mathematics in 1958 and a Ph.D. in mathematics in 1961, both from ETH Zurich. His thesis was in pure mathematics, but he then decided to go into statistics. He spent 1961--1963 as a postdoc at the statistics department in Berkeley where he wrote his first and most famous paper on robust statistics, ``Robust Estimation of a Location Parameter.'' After a position as a visiting professor at Cornell University, he became a full professor at ETH Zurich. He worked at ETH until 1978, interspersed by visiting positions at Cornell, Yale, Princeton and Harvard. After leaving ETH, he held professor positions at Harvard University 1978--1988, at MIT 1988--1992, and finally at the University of Bayreuth from 1992 until his retirement in 1999. He now lives in Klosters, a village in the Grisons in the Swiss Alps. Peter Huber has published four books and over 70 papers on statistics and data analysis. In addition, he has written more than a dozen papers and two books on Babylonian mathematics, astronomy and history. In 1972, he delivered the Wald lectures. He is a fellow of the IMS, of the American Association for the Advancement of Science, and of the American Academy of Arts and Sciences. In 1988 he received a Humboldt Award and in 1994 an honorary doctorate from the University of Neuch\^{a}tel. In addition to his fundamental results in robust statistics, Peter Huber made important contributions to computational statistics, strategies in data analysis, and applications of statistics in fields such as crystallography, EEGs, and human growth curves.Comment: Published in at http://dx.doi.org/10.1214/07-STS251 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

ChASE: Chebyshev Accelerated Subspace iteration Eigensolver for sequences of Hermitian eigenvalue problems

Solving dense Hermitian eigenproblems arranged in a sequence with direct solvers fails to take advantage of those spectral properties which are pertinent to the entire sequence, and not just to the single problem. When such features take the form of correlations between the eigenvectors of consecutive problems, as is the case in many real-world applications, the potential benefit of exploiting them can be substantial. We present ChASE, a modern algorithm and library based on subspace iteration with polynomial acceleration. Novel to ChASE is the computation of the spectral estimates that enter in the filter and an optimization of the polynomial degree which further reduces the necessary FLOPs. ChASE is written in C++ using the modern software engineering concepts which favor a simple integration in application codes and a straightforward portability over heterogeneous platforms. When solving sequences of Hermitian eigenproblems for a portion of their extremal spectrum, ChASE greatly benefits from the sequence's spectral properties and outperforms direct solvers in many scenarios. The library ships with two distinct parallelization schemes, supports execution over distributed GPUs, and it is easily extensible to other parallel computing architectures.Comment: 33 pages. Submitted to ACM TOM

The Orthogonal QD-Algorithm

The orthogonal qd-algorithm is presented to compute the singular value decomposition of a bidiagonal matrix. This algorithm represents a modification of Rutishauser's qd-algorithm, and it is capable of determining all the singular values to high relative precision. A generalization of the Givens transformation is also introduced, which has applications besides the orthogonal qd-algorithm. The shift strategy of the orthogonal qd-algorithm is based on Laguerre's method, which is used to compute a lower bound for the smallest singular value of the bidiagonal matrix. Special attention is devoted to the numerically stable evaluation of this shift. (Also cross-referenced as UMIACS-TR-94-9.1

Sensitivity of European glaciers to precipitation and temperature - two case studies

A nonlinear backpropagation network (BPN) has been trained with high-resolution multiproxy reconstructions of temperature and precipitation (input data) and glacier length variations of the Alpine Lower Grindelwald Glacier, Switzerland (output data). The model was then forced with two regional climate scenarios of temperature and precipitation derived from a probabilistic approach: The first scenario ("no change”) assumes no changes in temperature and precipitation for the 2000-2050 period compared to the 1970-2000 mean. In the second scenario ("combined forcing”) linear warming rates of 0.036-0.054°C per year and changing precipitation rates between −17% and +8% compared to the 1970-2000 mean have been used for the 2000-2050 period. In the first case the Lower Grindelwald Glacier shows a continuous retreat until the 2020s when it reaches an equilibrium followed by a minor advance. For the second scenario a strong and continuous retreat of approximately −30m/year since the 1990s has been modelled. By processing the used climate parameters with a sensitivity analysis based on neural networks we investigate the relative importance of different climate configurations for the Lower Grindelwald Glacier during four well-documented historical advance (1590-1610, 1690-1720, 1760-1780, 1810-1820) and retreat periods (1640-1665, 1780-1810, 1860-1880, 1945-1970). It is shown that different combinations of seasonal temperature and precipitation have led to glacier variations. In a similar manner, we establish the significance of precipitation and temperature for the well-known early eighteenth century advance and the twentieth century retreat of Nigardsbreen, a glacier in western Norway. We show that the maritime Nigardsbreen Glacier is more influenced by winter and/or spring precipitation than the Lower Grindelwald Glacie