WorldCat Identities

Bürgisser, Peter 1962-

Overview
Works: 42 works in 107 publications in 3 languages and 1,675 library holdings
Roles: Author, Other, dgs, Contributor, htt
Publication Timeline
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Most widely held works by Peter Bürgisser
Condition : the geometry of numerical algorithms by Peter Bürgisser( )

16 editions published in 2013 in 3 languages and held by 579 WorldCat member libraries worldwide

This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance --regarding both stability and complexity-- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming
Algebraic complexity theory by Peter Bürgisser( Book )

21 editions published between 1997 and 2011 in English and held by 436 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
Completeness and reduction in algebraic complexity theory by Peter Bürgisser( Book )

20 editions published between 1998 and 2011 in English and German and held by 320 WorldCat member libraries worldwide

"The theory of NP-completeness is a cornerstone of computational complexity. This monograph provides a thorough and comprehensive treatment of this concept in the framework of algebraic complexity theory. Many of the results presented are new and published for the first time. Topics include: complete treatment of Valiant's algebraic theory of NP-completeness, interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity, fast evaluation of representations of general linear groups, and complexity of immanants. The book can be used at the advanced undergraduate or at the beginning graduate level in either mathematics or computer science."--Jacket
Algebraic Complexity Theory : With the Collaboration of Thomas Lickteig by Peter Bürgisser( )

3 editions published in 1997 in English and German and held by 88 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
Degenerationsordnung und Trägerfunktional bilinearer Abbildungen by Peter Bürgisser( Book )

4 editions published between 1990 and 2006 in German and held by 29 WorldCat member libraries worldwide

Conjunctive queries, arithmetic circuits and counting complexity by Stefan Mengel( )

1 edition published in 2013 in English and held by 29 WorldCat member libraries worldwide

This thesis deals with several subjects from counting complexity and arithmetic circuit complexity.The first part explores the complexity of counting solutions to conjunctive queries, which are a basic class of queries from database theory. We introduce a parameter, called the quantified star size of a query phi, which measures how the free variables are spread in phi. As usual in database theory, we associate a hypergraph to a query phi. We show that for classes of queries for which these associated hypergraphs have bounded generalized hypertree width, bounded quantified star size exactly characterizes the subclasses of queries for which counting the number of solutions is tractable. In the case of bounded arity, this allows us to fully characterize the classes of conjunctive queries for which counting the solutions is tractable. Finally, we also analyze the complexity of computing the quantified star size of a conjunctive query.In the second part we characterize different classes from arithmetic circuit complexity by different means, including conjunctive queries and constraint satisfaction problems, graph polynomials on bounded treewidth graphs, and an extension of the classical arithmetic branching program model by stack memory.In particular, this yields new characterizations of the arithmetic circuit class VP, a class that is central to the area but arguably not well understood.Finally, the third part studies the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of its monomials. We show that these problems are complete for different levels of the counting hierarchy, which had few or no known natural complete problems before. ; eng
Condition : the geometry of numerical algorithms by Peter Bürgisser( )

1 edition published in 2013 in English and held by 23 WorldCat member libraries worldwide

This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance --regarding both stability and complexity-- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming
Geometric analysis of the condition of the convex feasibility problem by Dennis Amelunxen( )

1 edition published in 2011 in English and held by 18 WorldCat member libraries worldwide

Den Mittelpunkt dieser Arbeit bildet das homogene konvexe Lösbarkeitsproblem, welches die folgende Frage ist: Gegeben sei ein m-dimensionaler Unterraum des R n; schneidet dieser Unterraum einen gegebenen konvexen Kegel nur im Ursprung, oder gibt es weitere Schnittpunkte? Dieses Problem umfasst als Spezialfälle das lineare,das quadratische, und das semidefinite Lösbarkeitsproblem, wobei man als konvexen Kegel den positiven Orthanten, ein Produkt von Lorentzkegeln, bzw. den Kegel der positiv semidefiniten Matrizen wählt. Für die Laufzeit von Algorithmen, welche das konvexe Lösbarkeitsproblem lösen, spielt die Renegarsche Konditionszahl eine wichtige Rolle. Die Kondition einer Eingabe, bzw. ihr Inverses, ist gegeben durch die Größe einer kleinsten Störung, welche den Status der Eingabe von 'feasible' zu'infeasible' bzw. von 'infeasible' zu 'feasible' ändert. Wir werden eine Durchschnittsanalyse dieser Kondition für verschiedene Klassen von konvexen Kegeln angeben, sowie eine, welche unabhängig ist von der Wahl des zugrunde gelegten konvexen Kegels. Wir werden desweiteren einen Weg beschreiben, auf dem auch geglättete Analysen mittels unseres Ansatzes erzielt werden können. Wir erreichen diese Ergebnisse mit Hilfe einer rein geometrischen Sichtweise, welche zu Berechnungen in der Grassmann-Mannigfaltigkeit führt. Neben diesen Hauptergebnissen über das zufällige Verhalten der Kondition des konvexen Lösbarkeitsproblems werden wir auch einige Nebenergebnisse im Bereich der sphärischen Konvexgeometrie erzielen. ; ger
Isotropic and coisotropic subvarieties of Grassmannians by Kathlén Kohn( )

1 edition published in 2018 in English and held by 18 WorldCat member libraries worldwide

Condition : the Geometry of Numerical Algorithms by Peter Bürgisser( )

1 edition published in 2013 in English and held by 17 WorldCat member libraries worldwide

Numerical and statistical aspects of tensor decompositions by Paul Breiding( )

1 edition published in 2017 in English and held by 15 WorldCat member libraries worldwide

On the complexity of numerical analysis( )

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

Geometric complexity theory and orbit closures of homogeneous forms by Jesko Hüttenhain( )

1 edition published in 2017 in English and held by 13 WorldCat member libraries worldwide

Completeness and Reduction in Algebraic Complexity Theory by Peter Bürgisser( )

in English and held by 7 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

We prove a general lower bound on the average decision complexity for testing membership in an irreducible algebraic subset X [union] [real numbers][superscript m] and apply it to k-generic complete intersection of polynomials of the same degree, extending results in [4, 6]. We also give applications to nongeneric cases, such as graphs of elementary symmetric functions, SL(m, [real numbers]), and determinant varieties, extending results in [Li 90]."
Algebraic Complexity Theory : With the Collaboration of Thomas Lickteig by Peter Bürgisser( )

in English and held by 7 WorldCat member libraries worldwide

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
La double illusion de l'or et de l'amour chez Villiers de l'Isle-Adam by Peter Bürgisser( Book )

1 edition published in 1969 in French and held by 5 WorldCat member libraries worldwide

Decision complexity of generic complete intersections by Peter Bürgisser( Book )

1 edition published in 1992 in German and held by 5 WorldCat member libraries worldwide

Geometric complexity theory, tensor rank, and Littlewood-Richardson coefficients by Christian Ikenmeyer( )

2 editions published in 2012 in English and held by 4 WorldCat member libraries worldwide

We provide a thorough introduction to Geometric Complexity Theory, an approach towards computational complexity lower bounds via methods from algebraic geometry and representation theory. Then we focus on the relevant representation theoretic multiplicities, namely plethysm coefficients, Kronecker coefficients, and Littlewood-Richardson coefficients. These multiplicities can be described as dimensions of highest weight vector spaces for which explicit bases are known only in the Littlewood-Richardson case.By explicit construction of highest weight vectors we can show that the border rank of m x m matrix multiplication is a least 3 m 2 - 2 and the border rank of 2 x 2 matrix multiplication is exactly seven. The latter gives a new proof of a result by Landsberg (J. Amer. Math. Soc., 19:447-459, 2005).Moreover, we obtain new nonvanishing results for rectangular Kronecker coefficients and we prove a conjecture by Weintraub (J. Algebra, 129 (1): 103-114, 1990) about the nonvanishing of plethysm coefficients of even partitions.Our in-depth study of Littlewood-Richardson coefficients c_{\lambda,\mu} \nu yields a polynomial time algorithm for deciding c_{\lambda,\mu} \nu >= t in time polynomial in n and quadratic in t, where n denotes the number of parts of \nu. For t = 1, i.e., for checking positivity of c_{\lambda,\mu} \nu, we even obtain a running time of n 3 log \nu_1.Moreover, our insights lead to a proof of a conjecture by King, Tollu, and Toumazet (CRM Proc. Lecture Notes, 34, Symmetry in Physics: 99-112), stating that c_{\lambda,\mu} \nu = 2 implies c_{M\lambda,M\mu} {M\nu} = M + 1 for all M \in \N. ; eng
 
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Algebraic complexity theory
Covers
Algebraic complexity theoryCompleteness and reduction in algebraic complexity theoryCondition : the Geometry of Numerical Algorithms
Alternative Names
Burgisser, P.

Bürgisser, P. 1962-

Peter Bürgisser German mathematician and theoretical computer scientist

Peter Bürgisser mathématicien

Peter Bürgisser wiskundige

Languages
English (71)

German (11)

French (1)