De Boor, Carl
Overview
Works:  107 works in 525 publications in 7 languages and 5,054 library holdings 

Genres:  Conference papers and proceedings Handbooks and manuals Periodicals 
Roles:  Author, Editor 
Classifications:  QA297, 519.4 
Publication Timeline
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Most widely held works about
Carl De Boor
 [Oral History Program interview with Carl De Boor, 2007] by Carl De Boor( Recording )
Most widely held works by
Carl De Boor
Elementary numerical analysis; an algorithmic approach by
Samuel Daniel Conte(
Book
)
66 editions published between 1965 and 1995 in 3 languages and held by 1,421 WorldCat member libraries worldwide
Number systems and errors; The solution of nonlinear equations; Interpolation and approximation; Differentiation and integration; Matrices and systems of linear equations; The solution of differential equations; Boundaryvalue problems in ordinary differential equations
66 editions published between 1965 and 1995 in 3 languages and held by 1,421 WorldCat member libraries worldwide
Number systems and errors; The solution of nonlinear equations; Interpolation and approximation; Differentiation and integration; Matrices and systems of linear equations; The solution of differential equations; Boundaryvalue problems in ordinary differential equations
A practical guide to splines by
Carl De Boor(
Book
)
37 editions published between 1978 and 2008 in 3 languages and held by 1,199 WorldCat member libraries worldwide
37 editions published between 1978 and 2008 in 3 languages and held by 1,199 WorldCat member libraries worldwide
Mathematical aspects of finite elements in partial differential equations : proceedings of a symposium conducted by the Mathematics
Research Center, the University of WisconsinMadison, April 13, 1974 by
Carl De Boor(
Book
)
23 editions published between 1974 and 2014 in English and Undetermined and held by 395 WorldCat member libraries worldwide
Mathematical Aspects of Finite Elements in Partial Differential Equations addresses the mathematical questions raised by the use of finite elements in the numerical solution of partial differential equations. This book covers a variety of topics, including finite element method, hyperbolic partial differential equation, and problems with interfaces.Organized into 13 chapters, this book begins with an overview of the class of finite element subspaces with numerical examples. This text then presents as models the Dirichlet problem for the potential and bipotential operator and discusses the ques
23 editions published between 1974 and 2014 in English and Undetermined and held by 395 WorldCat member libraries worldwide
Mathematical Aspects of Finite Elements in Partial Differential Equations addresses the mathematical questions raised by the use of finite elements in the numerical solution of partial differential equations. This book covers a variety of topics, including finite element method, hyperbolic partial differential equation, and problems with interfaces.Organized into 13 chapters, this book begins with an overview of the class of finite element subspaces with numerical examples. This text then presents as models the Dirichlet problem for the potential and bipotential operator and discusses the ques
Recent advances in numerical analysis : proceedings of a symposium conducted by the Mathematics Research Center, the University
of WisconsinMadison, May 2224, 1978 by
Gene H Golub(
Book
)
28 editions published between 1978 and 1979 in English and Undetermined and held by 392 WorldCat member libraries worldwide
Recent Advances in Numerical Analysis
28 editions published between 1978 and 1979 in English and Undetermined and held by 392 WorldCat member libraries worldwide
Recent Advances in Numerical Analysis
Box splines by
Carl De Boor(
Book
)
12 editions published between 1993 and 2010 in English and Undetermined and held by 389 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
12 editions published between 1993 and 2010 in English and Undetermined and held by 389 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
Approximation theory by
Carl De Boor(
Book
)
21 editions published between 1986 and 2014 in English and held by 352 WorldCat member libraries worldwide
21 editions published between 1986 and 2014 in English and held by 352 WorldCat member libraries worldwide
Selected papers by
I. J Schoenberg(
Book
)
8 editions published in 1988 in English and held by 142 WorldCat member libraries worldwide
8 editions published in 1988 in English and held by 142 WorldCat member libraries worldwide
Splinefunktionen by
Carl De Boor(
Book
)
9 editions published between 1984 and 1990 in 3 languages and held by 91 WorldCat member libraries worldwide
Der Begriff der Splinefunktionen wurde von I.J. Schoenberg 1946 eingefUhrt. "Spline" ist der Name eines Zeichengerates, welches auf mechanischem Weg Interpolatio aufgaben lost. Dieses Gerat besteht aus einer flexiblen, oft mehrere Meter langen Latte, die auf dem Zeichenbrett aufliegt und dort an bestimmten Stellen durch Gewichte festgehalten wird. Die Form, die die Latte annimmt, hangt von den Elastizitatseigenschaften der Latte abo , ", \, \ \ I, ""', J::>", I I, I I I, ") Fig. 1: Latteninterpo1ation Po1ynominterpo1ation _        0 Wir konnen natUrlich versuchen, ein mathematisches Modell fUr dieses mechanische Zeichengerat zu machen, d. h. die Gestalt solcher Kurven mathematisch zu erfassen.  2  Die Theorie der Balkenbiegung verlangt, dass die mittlere 2 K quadratische KrUmmung, ("strain energy", Spannungs J energie) minimiert wird. Lasst sich die Kurve als Graph einer Funktion f auf dem Intervall [a, b] schreiben, so erhalt man mit dem bekannten Ausdruck fUr die Krlimmung K [f" (t) P dt ~ min (1) t [1 +f' (t)2J5/2 a Statt dieses schwierige Extremalproblem zu losen, begnUgt man sich damit, (2) zu minimieren. Die Extremalfunktion fUr das Funktional (2) ist stUckweise ein kubisches Polynom; die Polyn stUcke gehen an den Bruchstellen so glatt ineinander Uber, dass die Funktion zweimal stetig differenzierbar ist
9 editions published between 1984 and 1990 in 3 languages and held by 91 WorldCat member libraries worldwide
Der Begriff der Splinefunktionen wurde von I.J. Schoenberg 1946 eingefUhrt. "Spline" ist der Name eines Zeichengerates, welches auf mechanischem Weg Interpolatio aufgaben lost. Dieses Gerat besteht aus einer flexiblen, oft mehrere Meter langen Latte, die auf dem Zeichenbrett aufliegt und dort an bestimmten Stellen durch Gewichte festgehalten wird. Die Form, die die Latte annimmt, hangt von den Elastizitatseigenschaften der Latte abo , ", \, \ \ I, ""', J::>", I I, I I I, ") Fig. 1: Latteninterpo1ation Po1ynominterpo1ation _        0 Wir konnen natUrlich versuchen, ein mathematisches Modell fUr dieses mechanische Zeichengerat zu machen, d. h. die Gestalt solcher Kurven mathematisch zu erfassen.  2  Die Theorie der Balkenbiegung verlangt, dass die mittlere 2 K quadratische KrUmmung, ("strain energy", Spannungs J energie) minimiert wird. Lasst sich die Kurve als Graph einer Funktion f auf dem Intervall [a, b] schreiben, so erhalt man mit dem bekannten Ausdruck fUr die Krlimmung K [f" (t) P dt ~ min (1) t [1 +f' (t)2J5/2 a Statt dieses schwierige Extremalproblem zu losen, begnUgt man sich damit, (2) zu minimieren. Die Extremalfunktion fUr das Funktional (2) ist stUckweise ein kubisches Polynom; die Polyn stUcke gehen an den Bruchstellen so glatt ineinander Uber, dass die Funktion zweimal stetig differenzierbar ist
Spline toolbox for use with MATLAB : user's guide by
Carl De Boor(
Book
)
15 editions published between 1990 and 2004 in English and held by 42 WorldCat member libraries worldwide
15 editions published between 1990 and 2004 in English and held by 42 WorldCat member libraries worldwide
Análisis numérico elemental : un enfoque algorítmico by
Samuel Daniel Conte(
Book
)
6 editions published between 1972 and 1985 in Spanish and held by 22 WorldCat member libraries worldwide
6 editions published between 1972 and 1985 in Spanish and held by 22 WorldCat member libraries worldwide
Spline toolbox for use with MATLAB : user's guide, version 3 by
Carl De Boor(
Book
)
10 editions published between 1999 and 2005 in English and held by 13 WorldCat member libraries worldwide
10 editions published between 1999 and 2005 in English and held by 13 WorldCat member libraries worldwide
The Numerically Stable Reconstruction of a Jacobi Matrix from Spectral Data by
Carl De Boor(
Book
)
9 editions published in 1977 in English and Undetermined and held by 10 WorldCat member libraries worldwide
A stable algorithm is given for the construction of a symmetric tridiagonal matrix of order n from its eigenvalues and the eigenvalues of its upper left principal submatrix of order n  1. The algorithm might be of help in the approximate solution of inverse eigenvalue problems for SturmLiouville equations. (Author)
9 editions published in 1977 in English and Undetermined and held by 10 WorldCat member libraries worldwide
A stable algorithm is given for the construction of a symmetric tridiagonal matrix of order n from its eigenvalues and the eigenvalues of its upper left principal submatrix of order n  1. The algorithm might be of help in the approximate solution of inverse eigenvalue problems for SturmLiouville equations. (Author)
Analisis berangka permulaan : suatu pendekatan algoritma by
Samuel Daniel Conte(
Book
)
1 edition published in 1993 in Malay and held by 9 WorldCat member libraries worldwide
1 edition published in 1993 in Malay and held by 9 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
Extremal polynomials with application to Richardson iteration for indefinite linear systems by
Carl De Boor(
Book
)
5 editions published in 1980 in English and held by 8 WorldCat member libraries worldwide
The application of Richardson iteration to a symmetric, but indefinite linear system requires certain parameters which can be determined from the zeros in the error of a certain best polynomial approximant on some set S known to contain the spectrum of the coefficient matrix. It is pointed out that this error can also be obtained as a multiple of the extremal polynomial for the linear functional p at p(0), and this leads to an efficient Remes type algorithm for its determination. A program incorporating this algorithm for the case that S consists of two intervals bracketing zero is also given. (Author)
5 editions published in 1980 in English and held by 8 WorldCat member libraries worldwide
The application of Richardson iteration to a symmetric, but indefinite linear system requires certain parameters which can be determined from the zeros in the error of a certain best polynomial approximant on some set S known to contain the spectrum of the coefficient matrix. It is pointed out that this error can also be obtained as a multiple of the extremal polynomial for the linear functional p at p(0), and this leads to an efficient Remes type algorithm for its determination. A program incorporating this algorithm for the case that S consists of two intervals bracketing zero is also given. (Author)
Georgii Monachi Chronicon by
Georgius(
Book
)
2 editions published between 1904 and 1978 in Latin and Greek, Modern and held by 8 WorldCat member libraries worldwide
2 editions published between 1904 and 1978 in Latin and Greek, Modern 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
Package for calculating with bsplines by
Carl De Boor(
Book
)
5 editions published in 1973 in English and held by 7 WorldCat member libraries worldwide
ATIONS, FORTRAN, Polynomials, Subroutines, Theorems*Spline functions, Spline interpolation, Collocation(Mathematics)Eight FORTRAN subprograms for dealing computationally with piecewise polynomial functions (of one variable) are presented. The package is built around an algorithm for the stable evaluation of Bsplines of arbitrary order and with knots of arbitrary multiplicity. Four examples illustrate how one might use these routines: interpolation by splines of general order k (and not necessarily at the knots); least squares approximation by splines to discrete data; the determination of the derivative of a spline with respect to a knot; and the approximate solution of an ordinary differential equation with rather general side conditions by collocation. (Author)
5 editions published in 1973 in English and held by 7 WorldCat member libraries worldwide
ATIONS, FORTRAN, Polynomials, Subroutines, Theorems*Spline functions, Spline interpolation, Collocation(Mathematics)Eight FORTRAN subprograms for dealing computationally with piecewise polynomial functions (of one variable) are presented. The package is built around an algorithm for the stable evaluation of Bsplines of arbitrary order and with knots of arbitrary multiplicity. Four examples illustrate how one might use these routines: interpolation by splines of general order k (and not necessarily at the knots); least squares approximation by splines to discrete data; the determination of the derivative of a spline with respect to a knot; and the approximate solution of an ordinary differential equation with rather general side conditions by collocation. (Author)
Acta numerica(
Book
)
1 edition published in 1992 in English and held by 7 WorldCat member libraries worldwide
Presents information on "Acta Numerica," an annual publication from Cambridge University Press. Lists the members of the editorial board. Notes that the journal is a collection of review articles, including survey papers by leading researchers in numerical analysis and scientific computing. Offers instructions for contributors and the tables of contents for the current and previous issues
1 edition published in 1992 in English and held by 7 WorldCat member libraries worldwide
Presents information on "Acta Numerica," an annual publication from Cambridge University Press. Lists the members of the editorial board. Notes that the journal is a collection of review articles, including survey papers by leading researchers in numerical analysis and scientific computing. Offers instructions for contributors and the tables of contents for the current and previous issues
Inverses of infinite sign regular matrices by
Carl De Boor(
Book
)
5 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
Let A be an infinite sign regular (SR) matrix which can be viewed as a bounded linear operator from L sub infinity to itself. It is proved here that if the range of A contains the sequence (...,1,1,1,1 ...), then A is onto. If (inverse of A) exists then D (inverse of A) D is also SR, where D is the diagonal matrix with diagonal entries alternately 1 and 1. In case A is totally positive (TP), then D (inverse of A) D is also TP under additional assumptions on A. (Author)
5 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
Let A be an infinite sign regular (SR) matrix which can be viewed as a bounded linear operator from L sub infinity to itself. It is proved here that if the range of A contains the sequence (...,1,1,1,1 ...), then A is onto. If (inverse of A) exists then D (inverse of A) D is also SR, where D is the diagonal matrix with diagonal entries alternately 1 and 1. In case A is totally positive (TP), then D (inverse of A) D is also TP under additional assumptions on A. (Author)
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Related Identities
 Conte, Samuel Daniel 1917 Author
 University of WisconsinMadison Mathematics Research Center Other Editor
 Golub, Gene H. (Gene Howard) 19322007 Editor
 Höllig, Klaus Creator
 Riemenschneider, S. D. Creator
 American Mathematical Society Publisher
 Schoenberg, I. J. Author
 Trummer, Manfred R.
 WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
 MathWorks, Inc Other
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Algorithms Approximation theory Chebyshev polynomials Differential equations Differential equations, Partial Eigenvalues Electronic digital computers Finite element method FORTRAN (Computer program language) Fourier series Global analysis (Mathematics) History, Ancient Iterative methods (Mathematics) Jacobians Jacobi varieties Linear operators Mathematical analysis Mathematical analysisComputer programs Mathematics MATLAB Matrices Matrix inversion Multivariate analysis Numerical analysis Numerical analysisData processing Numerical calculations Orthogonal polynomials Polynomials Programming (Mathematics) Spectral sequences (Mathematics) Splines Spline theory Spline theoryData processing Timeseries analysis Universities and collegesFaculty University of WisconsinMadison
Alternative Names
Boor, C. de.
Boor Carl De
Boor, Carl de 1937
Boor, CarlWilhelm Reinhold de 1937
Carl de Boor
Carl de Boor deutschamerikanischer Mathematiker
Carl R. de Boor Amerikaans wiskundige
Carl R. de Boor matemático estadounidense
Carl R. de Boor matematico statunitense
Carl R. de Boor mathématicien américain
De Boor, C.
De Boor, C. 1937
De Boor, C. (Carl)
De Boor, C. (Carl), 1937
De Boor, CarlWilhelm Reinhold 1937
De Boor, Karl.
De Bor, K.
De Bor, K. 1937
De Bor, K. (Karl)
De Bor, K. (Karl), 1937
De Bor, Karl
De Bor, Karl 1937
DeBoor, Carl 1937
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