WorldCat Identities

Lickteig, Thomas

Overview
Works: 16 works in 29 publications in 3 languages and 127 library holdings
Roles: Author, Contributor, Thesis advisor, Other, Editor
Publication Timeline
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Most widely held works by Thomas Lickteig
Algebraic complexity theory by Peter Bürgisser( Book )

6 editions published between 1997 and 2010 in English and held by 43 WorldCat member libraries worldwide

This is the first book to present an up-to-date and self-contained account of Algebraic Complexity Theory that is both comprehensive and unified. Requiring of the reader only some basic algebra and offering over 350 exercises, it is well-suited as a textbook for beginners at graduate level. With its extensive bibliography covering about 500 research papers, this text is also an ideal reference book for the professional researcher. The subdivision of the contents into 21 more or less independent chapters enables readers to familiarize themselves quickly with a specific topic, and facilitates the use of this book as a basis for complementary courses in other areas such as computer algebra
Untersuchungen zum Tensorrangproblem by Thomas Lickteig( Book )

3 editions published in 1982 in German and held by 32 WorldCat member libraries worldwide

Dagstuhl-Seminar (Nr. 04061) on Real Computation and Complexity IBFI Schloss Dagstuhl, February 1 - 6, 2004( )

1 edition published in 2006 in English and held by 14 WorldCat member libraries worldwide

Real computation and complexity 04061 abstracts collection ; Dagstuhl seminar( )

1 edition published in 2006 in English and held by 14 WorldCat member libraries worldwide

On randomized algebraic test complexity by Peter Bürgisser( Book )

2 editions published in 1992 in German and English and held by 7 WorldCat member libraries worldwide

Abstract: "We investigate the impact of randomization on the complexity of deciding membership in a (semi- )algebraic subset X [union] [real numbers][superscript m]. Examples are exhibited where allowing for a certain error probability [epsilon] in the answer of the algorithms the complexity of decision problems decreases. A randomized ([omega][superscript k], [=, [less than or equal to]])-decision tree (k [union] [real numbers] a subfield) over m will be defined as a pair (T, [mu]) where [mu] a probability measure on some [real numbers][superscript n] and T is a ([omega][superscript k], [=, [less than or equal to]])- decision tree over m + n
Some computational problems in linear algebra as hard as matrix multiplication by Peter Bürgisser( Book )

4 editions published in 1991 in German and English and held by 6 WorldCat member libraries worldwide

Abstract: "We define the complexity of a computational problem given by a relation using the model of computation trees together with the Ostrowski complexity measure. Natural examples from linear algebra are: KER[subscript n]: Compute a basis of the kernel for a given n x n--matrix, OGB [subscript n]: Find an invertible matrix that transforms a given symmetric n x n--matrix (quadratic form) to diagonal form, SPR[subscript n]: Find a sparse representation of a given n x n--matrix. To such a sequence of problems we assign an exponent similar as for matrix multiplication
Untersuchungen zum Tensorrangproplem by Thomas Lickteig( Book )

1 edition published in 1982 in German and held by 2 WorldCat member libraries worldwide

Contributions vers l'accélération de l'algorithme de Buchberger en combinant la méthode de coupure de Knuth-Schönhage et une approche de type sous-résultants by Cyril Vervoux( Book )

2 editions published in 2002 in French and held by 2 WorldCat member libraries worldwide

Le but de cette thèse est l'amélioration du calcul des bases de Gröbner. Dans cet esprit, nous proposons une méthode combinant les sous-résultants et une stratégie "divide and conquer" basée sur la méthode de coupure de Knuth-Schönhage. Un progrès majeur pour le calcul des bases de Gröbner serait une implémentation d'une telle méthode sur une plateforme appropriée telle la machine du Turing multi-bande de Schönehage qui n'est pas handicapée par les limites de la RAM. Dans ce contexte surviennent de nombreuses questions techniques. Avec l'idée d'avoir finalement une approche basée sur une substitution à la Kronecker pour traiter les polynômes multivariés, nous présentons une perspective positive pour un futur algorithme rapide de bases de Gröbner et les bases concrètes d'un tel algorithme dans le cadre des polynômes univariés. En fait, les résultats sont un algorithme des sous-résultants pour plusieurs polynômes, prouvé dans les cas génériques et qui marche bien expérimentalement dans tous les cas (y compris les cas non génériques), et un algorithme "divide and conquer" d'élimination sur plusieurs polynômes utilisant à la fois l'approche des sous-résultants et une méthode de coupure. Une implémentation en Magma révèle la supériorité de l'approche combinée sous-résultants et méthode de coupure, déjà pour des polynômes de degré environ 700 pour trois polynômes (et 1250 pour cinq polynômes), et montre ainsi clairement un fort potentiel pour le développement futur de cette approche. Enfin, cette thèse amène de nombreuses questions ouvertes qui sont à résoudre pour atteindre le but initialement fixé
Real computation and complexity by Felipe Cucker( Book )

2 editions published between 1995 and 1996 in English and held by 1 WorldCat member library worldwide

Real computation and complexity : Dagstuhl-Seminar, 14-19.06.1998 by Felipe Cucker( Book )

1 edition published in 1998 in English and held by 1 WorldCat member library worldwide

Verification complexity of linear prime ideals by Peter Bürgisser( Book )

1 edition published in 1991 in English and held by 1 WorldCat member library worldwide

Ein elementarer Beweis fuer eine geometrische Gradschranke fuer die Zahl der Operationen bei der Berechnung von Polynomen by Thomas Lickteig( Book )

1 edition published in 1980 in German and held by 1 WorldCat member library worldwide

Test complexity of generic polynomials by Peter Bürgisser( Book )

1 edition published in 1991 in English and held by 1 WorldCat member library worldwide

Some computational problems in linear algebra as hard as matrix multiplication by Peter Bürgisser( Book )

1 edition published in 1991 in English and held by 1 WorldCat member library worldwide

Real computation and complexity( Book )

1 edition published in 2000 in English and held by 1 WorldCat member library worldwide

Contributions vers l'accélération de l'algorithme de Buchberger en combinant la méthode de coupure de Knuth-Schönhage et une approche de type sous-résultants by Cyril Vervoux( )

1 edition published in 2002 in French and held by 0 WorldCat member libraries worldwide

The goal of this thesis is the improvement of Gröbner bases computation
 
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Associated Subjects
Algebraic complexity theory
Covers
Languages
English (18)

German (8)

French (3)