Höllig, Klaus
Overview
Works:  52 works in 163 publications in 2 languages and 1,244 library holdings 

Roles:  Author, Other, Creator 
Classifications:  QA224, 511.42 
Publication Timeline
.
Most widely held works by
Klaus Höllig
Box splines by
Carl De Boor(
Book
)
13 editions published between 1993 and 2010 in English and Undetermined and held by 393 WorldCat member libraries worldwide
This book on box splines is the first book giving a complete development for any kind of multivariate spline. Box splines give rise to an intriguing and beautiful mathematical theory that is much richer and more intricate than the univariate case because of the complexity of smoothly joining polynomial pieces on polyhedral cells. The purpose of this book is to provide the basic facts about box splines in a cohesive way with simple, complete proofs, many illustrations, and with an uptodate bibliography. It is not the book's intention to be encyclopedic about the subject, but rather to provide the fundamental knowledge necessary to familiarize graduate students and researchers in analysis, numerical analysis, and engineering with a subject that surely will have as many widespread applications as its univariate predecessor. This book will be used as a supplementary text for graduate courses. The book begins with chapters on box splines defined, linear algebra of box spline spaces, and quasiinterpolants and approximation power. It continues with cardinal interpolation and difference equations, approximation by cardinal splines and wavelets. The book concludes with discrete box splines and linear diophantine equations, and subdivision algorithms
13 editions published between 1993 and 2010 in English and Undetermined and held by 393 WorldCat member libraries worldwide
This book on box splines is the first book giving a complete development for any kind of multivariate spline. Box splines give rise to an intriguing and beautiful mathematical theory that is much richer and more intricate than the univariate case because of the complexity of smoothly joining polynomial pieces on polyhedral cells. The purpose of this book is to provide the basic facts about box splines in a cohesive way with simple, complete proofs, many illustrations, and with an uptodate bibliography. It is not the book's intention to be encyclopedic about the subject, but rather to provide the fundamental knowledge necessary to familiarize graduate students and researchers in analysis, numerical analysis, and engineering with a subject that surely will have as many widespread applications as its univariate predecessor. This book will be used as a supplementary text for graduate courses. The book begins with chapters on box splines defined, linear algebra of box spline spaces, and quasiinterpolants and approximation power. It continues with cardinal interpolation and difference equations, approximation by cardinal splines and wavelets. The book concludes with discrete box splines and linear diophantine equations, and subdivision algorithms
Finite element methods with Bsplines by
Klaus Höllig(
Book
)
13 editions published between 2003 and 2012 in English and Undetermined and held by 216 WorldCat member libraries worldwide
The finite element method (FEM) has become the most widely accepted generalpurpose technique for numerical simulations in engineering and applied mathematics. Principal applications arise in continuum mechanics, fluid flow, thermodynamics and field theory. In these areas, computational methods are essential and benefit strongly from the enormous advances in computer technology. Bsplines play an important role in approximation and geometric modeling. They are used in data fitting, computeraided design (CAD), automated manufacturing (CAM) and computer graphics. Finite Element Methods with BSplines describes new weighted approximation techniques, combining the computational advantages of Bsplines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often timeconsuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction and elasticity
13 editions published between 2003 and 2012 in English and Undetermined and held by 216 WorldCat member libraries worldwide
The finite element method (FEM) has become the most widely accepted generalpurpose technique for numerical simulations in engineering and applied mathematics. Principal applications arise in continuum mechanics, fluid flow, thermodynamics and field theory. In these areas, computational methods are essential and benefit strongly from the enormous advances in computer technology. Bsplines play an important role in approximation and geometric modeling. They are used in data fitting, computeraided design (CAD), automated manufacturing (CAM) and computer graphics. Finite Element Methods with BSplines describes new weighted approximation techniques, combining the computational advantages of Bsplines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often timeconsuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction and elasticity
Approximation and modeling with Bsplines by
Klaus Höllig(
Book
)
7 editions published in 2013 in English and held by 91 WorldCat member libraries worldwide
Bsplines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of Bspline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems with solutions available for instructors, slides for use in lectures, and programs with demos. Audience: Approximation and Modeling with BSplines is appropriate as an advanced undergraduate or firstyear graduate text for courses on splines or approximation and geometric modeling for students in mathematics, engineering, and computer science. Practitioners in these fields who are using Bsplines in numerical simulations, computeraided design, and visualization will also find the book useful in their work. Amazon.com
7 editions published in 2013 in English and held by 91 WorldCat member libraries worldwide
Bsplines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of Bspline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems with solutions available for instructors, slides for use in lectures, and programs with demos. Audience: Approximation and Modeling with BSplines is appropriate as an advanced undergraduate or firstyear graduate text for courses on splines or approximation and geometric modeling for students in mathematics, engineering, and computer science. Practitioners in these fields who are using Bsplines in numerical simulations, computeraided design, and visualization will also find the book useful in their work. Amazon.com
Grundlagen der Numerik by
Klaus Höllig(
Book
)
1 edition published in 1998 in German and held by 30 WorldCat member libraries worldwide
1 edition published in 1998 in German and held by 30 WorldCat member libraries worldwide
BSplineApproximation elliptischer Randwertprobleme mit unstetigen Koeffizienten by
Andreas Keller(
)
1 edition published in 2013 in German and held by 16 WorldCat member libraries worldwide
1 edition published in 2013 in German and held by 16 WorldCat member libraries worldwide
Multivariate splines by
Klaus Höllig(
Book
)
9 editions published between 1981 and 1987 in English and Undetermined and held by 11 WorldCat member libraries worldwide
The purpose of this report is to introduce a class of multivariate non tensor product spline functions and study its basic properties
9 editions published between 1981 and 1987 in English and Undetermined and held by 11 WorldCat member libraries worldwide
The purpose of this report is to introduce a class of multivariate non tensor product spline functions and study its basic properties
Aufgaben und Lösungen zur Höheren Mathematik by
Klaus Höllig(
Book
)
1 edition published in 2017 in German and held by 10 WorldCat member libraries worldwide
1 edition published in 2017 in German and held by 10 WorldCat member libraries worldwide
Error estimates for the webmethod by
Klaus Höllig(
Book
)
4 editions published in 2000 in English and held by 9 WorldCat member libraries worldwide
4 editions published in 2000 in English and held by 9 WorldCat member libraries worldwide
Nonuniform WEBsplines by
Klaus Höllig(
Book
)
3 editions published in 2002 in English and held by 8 WorldCat member libraries worldwide
3 editions published in 2002 in English and held by 8 WorldCat member libraries worldwide
Bsplines without divided differences by
Carl De Boor(
Book
)
9 editions published in 1985 in English and Undetermined and held by 8 WorldCat member libraries worldwide
This note develops the basic Bspline theory without using divided differences. Instead, the starting point is the definition of Bsplines via recurrence relations. This approach yields very simple derivations of basic properties of spline functions and algorithms
9 editions published in 1985 in English and Undetermined and held by 8 WorldCat member libraries worldwide
This note develops the basic Bspline theory without using divided differences. Instead, the starting point is the definition of Bsplines via recurrence relations. This approach yields very simple derivations of basic properties of spline functions and algorithms
Nonuniform WEBSplines by
Klaus Höllig(
)
1 edition published in 2002 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 8 WorldCat member libraries worldwide
Convergence of cardinal series by
Carl De Boor(
Book
)
6 editions published in 1985 in English and held by 7 WorldCat member libraries worldwide
The result of this paper is a generalization of an characterization of the limits of multivariate cardinal splines. Keywords: Convergence; fourier transforms; Analytic functions; Convolution; Exponential functions; Fourier series
6 editions published in 1985 in English and held by 7 WorldCat member libraries worldwide
The result of this paper is a generalization of an characterization of the limits of multivariate cardinal splines. Keywords: Convergence; fourier transforms; Analytic functions; Convolution; Exponential functions; Fourier series
Mehrfeldprobleme in der Kontinuumsmechanik = Geometric hermite interpolation with maximal order and smoothness by
Klaus Höllig(
Book
)
1 edition published in 1996 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 1996 in English and held by 7 WorldCat member libraries worldwide
Divided differences, hyperbolic equations, and lifting distributions by
Klaus Höllig(
Book
)
4 editions published in 1985 in English and held by 6 WorldCat member libraries worldwide
4 editions published in 1985 in English and held by 6 WorldCat member libraries worldwide
Boxspline tilings by
Carl De Boor(
Book
)
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
Approximationszahlen von SobolevEinbettungen by
Klaus Höllig(
Book
)
3 editions published in 1979 in German and held by 5 WorldCat member libraries worldwide
3 editions published in 1979 in German and held by 5 WorldCat member libraries worldwide
Geometric hermite interpolation with maximal order and smoothness by
Klaus Höllig(
Book
)
2 editions published between 1995 and 1996 in English and held by 5 WorldCat member libraries worldwide
2 editions published between 1995 and 1996 in English and held by 5 WorldCat member libraries worldwide
A nonlinear integral equation occurring in a singular free boundary problem by
Klaus Höllig(
Book
)
5 editions published between 1983 and 1984 in English and held by 4 WorldCat member libraries worldwide
One motivation for the study of the Cauchy problem is its similarity with the wellknown one phase Stefan problem (in one space dimension). The principal motivation for the study of this problem is that it serves as a prototype of nonlinear parabolic problems which arise as monotone convexifications of nonlinear diffusion equations with nonmonotone constitutive functions phi
5 editions published between 1983 and 1984 in English and held by 4 WorldCat member libraries worldwide
One motivation for the study of the Cauchy problem is its similarity with the wellknown one phase Stefan problem (in one space dimension). The principal motivation for the study of this problem is that it serves as a prototype of nonlinear parabolic problems which arise as monotone convexifications of nonlinear diffusion equations with nonmonotone constitutive functions phi
Self Similar Solutions for a Degenerate Cauchy Problem by
Mathematics Research Center (United States. Army)(
Book
)
4 editions published between 1984 and 1985 in English and held by 4 WorldCat member libraries worldwide
In this article the authors determine the selfsimilar solutions of a Cauchy problem v sub t = psi(v) xx where x is an element of R when t> 0 and v(x,0) = g(x) for a constitutive function
4 editions published between 1984 and 1985 in English and held by 4 WorldCat member libraries worldwide
In this article the authors determine the selfsimilar solutions of a Cauchy problem v sub t = psi(v) xx where x is an element of R when t> 0 and v(x,0) = g(x) for a constitutive function
Box splines by
Klaus Höllig(
Book
)
3 editions published in 1986 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1986 in English and held by 4 WorldCat member libraries worldwide
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Associated Subjects
Algebra Algorithms Approximation theory Computer scienceMathematics Differential equations, Hyperbolic EngineeringMathematical models Finite element method Fourier series Global analysis (Mathematics) Interpolation Mathematical analysis Mathematical models Mathematics Multivariate analysis Numerical analysis Splines Spline theory Structural analysis (Engineering) Surfaces Tiling (Mathematics)