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Eduard Stiefel
Eduard L. Stiefel (21 April 1909 – 25 November 1978) was a Swiss mathematician. Together with Cornelius Lanczos and Magnus Hestenes, he invented the conjugate gradient method, and gave what is now understood to be a partial construction of the Stiefel–Whitney classes of a real vector bundle, thus co-founding the study of characteristic classes. Biography Stiefel entered the Swiss Federal Institute of Technology (ETH Zurich) in 1928. He received his Ph.D. in 1935 under Heinz Hopf; his dissertation was titled "Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten". Stiefel completed his habilitation in 1942. Besides his academic pursuits, Stiefel was also active as a military officer, rising to the rank of colonel in the Swiss army during World War II. Stiefel achieved his full professorship at ETH Zurich in 1943, founding the Institute for Applied Mathematics five years later. The objective of the new institute was to design and construct an elect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zürich
, neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, Opfikon, Regensdorf, Rümlang, Schlieren, Stallikon, Uitikon, Urdorf, Wallisellen, Zollikon , twintowns = Kunming, San Francisco Zürich () is the largest city in Switzerland and the capital of the canton of Zürich. It is located in north-central Switzerland, at the northwestern tip of Lake Zürich. As of January 2020, the municipality has 434,335 inhabitants, the urban area 1.315 million (2009), and the Zürich metropolitan area 1.83 million (2011). Zürich is a hub for railways, roads, and air traffic. Both Zurich Airport and Zürich's main railway station are the largest and busiest in the country. Permanently settled for over 2,000 years, Zürich was founded by the Romans, who called it '. However, early settlements have been found dating back more than 6,400 years (although this only indicates human presence in the area and not the presence of a town that early). During ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjugate Gradient Method
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems. The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, who programmed it on the Z4, and extensively researched it. The biconjugate gradient method provides a generalization to non-symmetric matrices. Various nonlinear conjugate gradient methods seek minima of nonlinear optimization problems. Description of the problem address ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Todd (computer Scientist)
John Todd (May 16, 1911 – June 21, 2007) was a Northern Irish mathematician most of whose career was spent in England and the USA; he was a pioneer in the field of numerical analysis. He was born in Carnacally, County Down, Ireland, and grew up near Belfast. He attended Methodist College Belfast after winning a scholarship. In his final year at the College he only studied maths as a result of his desire to become an engineer. He received his BSc degree from Queen's University in 1931, and went to St. John's College at Cambridge University, studying for 2 years with J. E. Littlewood, who advised him against getting a doctorate and just to do research. He taught at Queen's University Belfast 1933-1937, and was an invited speaker at the 1936 ICM in Oslo on "Transfinite Superpositions of Absolutely Continuous Functions" He worked at King's College in London for the years 1937–1939 (and again 1945–1947), where he met Olga Taussky, a matrix and number theorist (she had al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stiefel Manifold
In mathematics, the Stiefel manifold V_k(\R^n) is the set of all orthonormal ''k''-frames in \R^n. That is, it is the set of ordered orthonormal ''k''-tuples of vectors in \R^n. It is named after Swiss mathematician Eduard Stiefel. Likewise one can define the complex Stiefel manifold V_k(\Complex^n) of orthonormal ''k''-frames in \Complex^n and the quaternionic Stiefel manifold V_k(\mathbb^n) of orthonormal ''k''-frames in \mathbb^n. More generally, the construction applies to any real, complex, or quaternionic inner product space. In some contexts, a non- compact Stiefel manifold is defined as the set of all linearly independent ''k''-frames in \R^n, \Complex^n, or \mathbb^n; this is homotopy equivalent, as the compact Stiefel manifold is a deformation retract of the non-compact one, by Gram–Schmidt. Statements about the non-compact form correspond to those for the compact form, replacing the orthogonal group (or unitary or symplectic group) with the general linear group ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zurich
Zurich (; ) is the largest city in Switzerland and the capital of the canton of Zurich. It is located in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 443,037 inhabitants, the urban area 1.315 million (2009), and the Zurich metropolitan area 1.83 million (2011). Zurich is a hub for railways, roads, and air traffic. Both Zurich Airport and Zurich's main railway station are the largest and busiest in the country. Permanently settled for over 2,000 years, Zurich was founded by the Romans, who called it '. However, early settlements have been found dating back more than 6,400 years (although this only indicates human presence in the area and not the presence of a town that early). During the Middle Ages, Zurich gained the independent and privileged status of imperial immediacy and, in 1519, became a primary centre of the Protestant Reformation in Europe under the leadership of Huldrych Zwingli. The official language of Zurich is Germ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Bureau Of Standards
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical science laboratory programs that include nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement. From 1901 to 1988, the agency was named the National Bureau of Standards. History Background The Articles of Confederation, ratified by the colonies in 1781, provided: The United States in Congress assembled shall also have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective states—fixing the standards of weights and measures throughout the United States. Article 1, section 8, of the Constitution of the United States, ratified in 1789, granted these powers to the new Congre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., federal district, five major unincorporated territories, nine United States Minor Outlying Islands, Minor Outlying Islands, and 326 Indian reservations. The United States is also in Compact of Free Association, free association with three Oceania, Pacific Island Sovereign state, sovereign states: the Federated States of Micronesia, the Marshall Islands, and the Palau, Republic of Palau. It is the world's List of countries and dependencies by area, third-largest country by both land and total area. It shares land borders Canada–United States border, with Canada to its north and Mexico–United States border, with Mexico to its south and has maritime borders with the Bahamas, Cuba, Russia, and other nations. With a population of over 333 million, it is the List of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ERMETH
The ERMETH (Electronic Calculating Machine of the ETH) was one of the first computers in Europe and was developed and built by Eduard Stiefel and his team of the Institute for Applied Mathematics at the ETH Zurich between 1948 and 1956. It was in use until 1963 and is now displayed at the Museum of Communication Bern ( Switzerland). Models Eduard Stiefel and his two senior assistants Heinz Rutishauser and Ambros Speiser were inspired by models in the USA and United Kingdom when developing the ERMETH. In 1949 Rutishauser and Speiser undertook study trips to Howard Aiken (Harvard University), John von Neumann (Princeton University) and to the University of Cambridge, which operated the EDSAC. In 1950, Stiefel rented for five years the only existing digital computer in continental Europe at that time, the Zuse Z4, completed by Konrad Zuse in 1945, for the ETH in order to gain experience with a calculating machine during the construction of the ERMETH. Technical concept The ER ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seminar For Applied Mathematics
The Seminar for Applied Mathematics (SAM; from 1948 to 1969 Institute for Applied Mathematics) was founded in 1948 by Prof. Eduard Stiefel. It is part of the Department of Mathematics (D-MATH) of the Swiss Federal Institute of Technology, ETH Zurich. The Seminar consists of four regular professorships (as of 2014), two assistant professorships, two permanent senior scientists, approximately 14 positions for assistants which are either filled by senior assistants, postdoctoral fellows or Ph.D. students, as well as secretarial staff and a systems administrator. It is represented by the Head of SAM. The SAM is a center for research and teaching in numerical mathematics, mathematical modelling and computing in Science and Technology in the D-MATH of the ETH Zürich. Mission * To conduct fundamental research in the development and mathematical analysis of efficient discretizations for problems in engineering and the sciences as well as their implementation on supercomputers * To provid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies of World War II, Allies and the Axis powers. World War II was a total war that directly involved more than 100 million Military personnel, personnel from more than 30 countries. The major participants in the war threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. Air warfare of World War II, Aircraft played a major role in the conflict, enabling the strategic bombing of population centres and deploying the Atomic bombings of Hiroshima and Nagasaki, only two nuclear weapons ever used in war. World War II was by far the List of wars by death toll, deadliest conflict in hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a dissertation. The degree, abbreviated "Dr. habil." (Doctor habilitatus) or "PD" (for "Privatdozent"), is a qualification for professorship in those countries. The conferral is usually accompanied by a lecture to a colloquium as well as a public inaugural lecture. History and etymology The term ''habilitation'' is derived from the Medieval Latin , meaning "to make suitable, to fit", from Classical Latin "fit, proper, skillful". The degree developed in Germany in the seventeenth century (). Initially, habilitation was synonymous with "doctoral qualification". The term became synonymous with "post-doctoral qualification" in Germany in the 19th century "when holding a doctorate seemed no longer sufficient to guarantee a proficient transfe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ETH Zurich
(colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , academic_staff = 6,612 (including doctoral students, excluding 527 professors of all ranks, 34% female, 65% foreign nationals) (full-time equivalents 2021) , administrative_staff = 3,106 (40% female, 19% foreign nationals, full-time equivalents 2021) , students = 24,534 (headcount 2021, 33.3% female, 37% foreign nationals) , undergrad = 10,642 , postgrad = 8,299 , doctoral = 4,460 , other = 1,133 , address = Rämistrasse 101CH-8092 ZürichSwitzerland , city = Zürich , coor = , campus = Urban , language = German, English (Masters and upwards, sometimes Bachelor) , affiliations = CESAER, EUA, GlobalTech, IARU, IDEA League, UNITECH , website ethz.ch, colors = Black and White , logo = ETH Zürich Logo black.svg ETH Z� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
