Riemenschneider, S. D.
Overview
Works:  13 works in 68 publications in 2 languages and 2,137 library holdings 

Roles:  Author, Creator 
Publication Timeline
.
Most widely held works by
S. D Riemenschneider
Birkhoff interpolation by
G. G Lorentz(
)
28 editions published between 1983 and 2009 in English and Undetermined and held by 1,655 WorldCat member libraries worldwide
This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and interpolation in the last twenty years. It presents all the basic material known at the present time in a unified manner. Topics discussed include; applications of Birkhoff interpolation to approximation theory, quadrature formulas and Chebyshev systems; lacunary interpolation at special knots and an introduction to the theory of Birkhoff interpolation by splines
28 editions published between 1983 and 2009 in English and Undetermined and held by 1,655 WorldCat member libraries worldwide
This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and interpolation in the last twenty years. It presents all the basic material known at the present time in a unified manner. Topics discussed include; applications of Birkhoff interpolation to approximation theory, quadrature formulas and Chebyshev systems; lacunary interpolation at special knots and an introduction to the theory of Birkhoff interpolation by splines
Box splines by
Carl De Boor(
Book
)
13 editions published between 1993 and 2010 in English and Undetermined and held by 450 WorldCat member libraries worldwide
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. 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. This is the first book giving a complete development for any kind of multivariate spline. This book will be useful as a supplementary text for graduate courses
13 editions published between 1993 and 2010 in English and Undetermined and held by 450 WorldCat member libraries worldwide
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. 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. This is the first book giving a complete development for any kind of multivariate spline. This book will be useful as a supplementary text for graduate courses
Convergence of cardinal series by
Carl De Boor(
Book
)
4 editions published in 1985 in English and held by 5 WorldCat member libraries worldwide
4 editions published in 1985 in English and held by 5 WorldCat member libraries worldwide
Cardinal interpolation, submodules and the 4direction mesh by
K Jetter(
Book
)
3 editions published in 1986 in English and German and held by 5 WorldCat member libraries worldwide
3 editions published in 1986 in English and German and held by 5 WorldCat member libraries worldwide
Fundamental soulutions for multivariate difference equations and applications to cardinal interpolation by
Carl De Boor(
Book
)
4 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
Convergence of Bivariate Cardinal Interpolation by
Mathematics Research Center (United States. Army)(
Book
)
3 editions published in 1984 in English and held by 3 WorldCat member libraries worldwide
This is a followup on a previous report in which the authors introduced and studied interpolation by a linear combination of translates of a bivariate box spline on a threedirection mesh. This is of interest because these box splines are not just tensor products of univariate Bsplines but are genuinely bivariate, yet are true generalizations of the univariate cardinal Bspline. This allows one to be guided by Schoenberg's highly successful analysis of univariate cardinal splines, while at the same time struggling with a more complicated setup. The specific task of the present report is the derivation of necessary and of sufficient conditions for the convergence of the box spline interpolants as the degree goes to infinity. The conditions are stated in terms of the Fourier transform of the interpolant
3 editions published in 1984 in English and held by 3 WorldCat member libraries worldwide
This is a followup on a previous report in which the authors introduced and studied interpolation by a linear combination of translates of a bivariate box spline on a threedirection mesh. This is of interest because these box splines are not just tensor products of univariate Bsplines but are genuinely bivariate, yet are true generalizations of the univariate cardinal Bspline. This allows one to be guided by Schoenberg's highly successful analysis of univariate cardinal splines, while at the same time struggling with a more complicated setup. The specific task of the present report is the derivation of necessary and of sufficient conditions for the convergence of the box spline interpolants as the degree goes to infinity. The conditions are stated in terms of the Fourier transform of the interpolant
Some Qualitative Properties of Bivariate EulerFrobenius Polynomials by
Carl De Boor(
Book
)
3 editions published in 1984 in English and held by 3 WorldCat member libraries worldwide
This is a further report in a series devoted to the study of box splines. Box splines provide a natural generalization of univariate cardinal splines, i.e., splines with a uniform knot sequence. The process of univariate spline interpolation becomes particularly simple in the cardinal case, and this report considers the corresponding bivariate process of interpolation at the integer points in the plane to a given function by a linear combination of integer translates of a box spline. In particular, the report shows that this process is well posed, i.e., any bounded continuous function has exactly one such bounded interpolant If. The argument uses the Fourier transform to identify a certain trigonometric polynomial (in two variables) whose nonvanishing is equivalent to the asserted wellposedness. The minimum value of this polynomial yields a bound on the norm of the resulting interpolation projector I
3 editions published in 1984 in English and held by 3 WorldCat member libraries worldwide
This is a further report in a series devoted to the study of box splines. Box splines provide a natural generalization of univariate cardinal splines, i.e., splines with a uniform knot sequence. The process of univariate spline interpolation becomes particularly simple in the cardinal case, and this report considers the corresponding bivariate process of interpolation at the integer points in the plane to a given function by a linear combination of integer translates of a box spline. In particular, the report shows that this process is well posed, i.e., any bounded continuous function has exactly one such bounded interpolant If. The argument uses the Fourier transform to identify a certain trigonometric polynomial (in two variables) whose nonvanishing is equivalent to the asserted wellposedness. The minimum value of this polynomial yields a bound on the norm of the resulting interpolation projector I
Cardinal hermite interpolation with box splines by
S. D Riemenschneider(
Book
)
2 editions published in 1986 in German and English and held by 3 WorldCat member libraries worldwide
2 editions published in 1986 in German and English and held by 3 WorldCat member libraries worldwide
Birkhoff interpolation by
G. G Lorentz(
Book
)
2 editions published in 1984 in Undetermined and held by 3 WorldCat member libraries worldwide
2 editions published in 1984 in Undetermined and held by 3 WorldCat member libraries worldwide
Convergence of Cardinal Series by
Mathematics Research Center (United States. Army)(
Book
)
2 editions published in 1985 in English and held by 2 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
2 editions published in 1985 in English and held by 2 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
Bivariate Cardinal Interpolation by Splines on a ThreeDirection Mesh by
United States(
Book
)
2 editions published in 1983 in English and held by 2 WorldCat member libraries worldwide
In a series of monographs Schogenberg developed a comprehensive theory of univariate cardinal splines. His results strongly influenced the analysis of totally positive matrices. In this report the author extend two of his basic results on cardinal interpolation to bivariate boxsplines. They show that, for functions of exponential type, cardinal interpolation is a rapidly convergent approximation process as the degree tends to infinity. Being not restricted to a tensor product mesh gives a greater flexibility, and because of the exponential decay of the Lagrange functions, spline interpolation is suitable, e.g., for data smoothing. They also expect that bivariate cardinal splines have a similar significance for theoretical questions as in the univariate case
2 editions published in 1983 in English and held by 2 WorldCat member libraries worldwide
In a series of monographs Schogenberg developed a comprehensive theory of univariate cardinal splines. His results strongly influenced the analysis of totally positive matrices. In this report the author extend two of his basic results on cardinal interpolation to bivariate boxsplines. They show that, for functions of exponential type, cardinal interpolation is a rapidly convergent approximation process as the degree tends to infinity. Being not restricted to a tensor product mesh gives a greater flexibility, and because of the exponential decay of the Lagrange functions, spline interpolation is suitable, e.g., for data smoothing. They also expect that bivariate cardinal splines have a similar significance for theoretical questions as in the univariate case
Some properties of linear operators on LP and Lorentz spaces by
S. D Riemenschneider(
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Convergence of Lacunary Trigonometric Interpolation on Equidistant Nodes(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Jetter, K. Author
 Lorentz, G. G. Author
 Höllig, Klaus Creator
 De Boor, Carl Author
 Boor, Carl Author
 Boor, Carl de Author
 WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
 Scherer, Karl
 Mathematics Research Center (United States. Army)
 De Boor, Carl