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Author: Thomas Nall Eden Greville Publisher: ISBN: Category : Spline theory Languages : en Pages : 31
Book Description
A more compact reformulation (probably not generalizable to higher degrees) is given of Schoenberg's explicit construction of interpolating cubic splines with equidistant nodes. (Author).
Author: Thomas Nall Eden Greville Publisher: ISBN: Category : Spline theory Languages : en Pages : 31
Book Description
A more compact reformulation (probably not generalizable to higher degrees) is given of Schoenberg's explicit construction of interpolating cubic splines with equidistant nodes. (Author).
Author: I. J. Schoenberg Publisher: ISBN: Category : Interpolation Languages : en Pages : 59
Book Description
For both natural and complete equidistant cubic spline interpolation the respective interpolating spline is explicitly constructed in terms of cubic B-splines. (Author).
Author: Gary D. Knott Publisher: Springer Science & Business Media ISBN: 1461213207 Category : Computers Languages : en Pages : 247
Book Description
A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav els side-by-side with the art of automobile design, sail construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.
Author: I. J. Schoenberg Publisher: SIAM ISBN: 9781611970555 Category : Mathematics Languages : en Pages : 131
Book Description
As this monograph shows, the purpose of cardinal spline interpolation is to bridge the gap between the linear spline and the cardinal series. The author explains cardinal spline functions, the basic properties of B-splines, including B- splines with equidistant knots and cardinal splines represented in terms of B-splines, and exponential Euler splines, leading to the most important case and central problem of the book-- cardinal spline interpolation, with main results, proofs, and some applications. Other topics discussed include cardinal Hermite interpolation, semi-cardinal interpolation, finite spline interpolation problems, extremum and limit properties, equidistant spline interpolation applied to approximations of Fourier transforms, and the smoothing of histograms.
Author: Thomas Maindl Publisher: Createspace Independent Publishing Platform ISBN: 9781987487374 Category : Languages : en Pages : 90
Book Description
This textbook will enable you to - discuss polynomial and spline interpolation - explain why using splines is a good method for interpolating data - construct cubic interpolating splines for your own projects It is a self-contained course for students who wish to learn about interpolating cubic splines and for lecturers who seek inspiration for designing a spline interpolation module. The book's innovative concept combines - a slide-based lecture with textual notes - a thorough introduction to the mathematical formalism - exercises - a "rocket science" project that implements constructing interpolating splines in Python for answering questions about the velocity, g-force, and covered distance after the first launch of SpaceX(R)' Falcon(R) Heavy Target group: STEM (science, technology, engineering, and math) students and lecturers at colleges and universities Contents: Preface 1 Cubic spline interpolation 2 Mini-script for constructing cubic splines 3 Spline exercises 4 The rocket launch project 5 Closing remarks Appendix A notebook for periodic cubic splines Index
Author: James B. Cheek Publisher: ISBN: Category : Curve fitting Languages : en Pages : 62
Book Description
This paper was prepared to familiarize practicing scientists and engineers with the cubic spline interpolation technique as a possible tool in curve fitting for computer programs for which more commonly used techniques may be unsuitable or of limited value. The spline technique is compared with more common methods, specifically piecewise linear and polynomial, and examples of applications of the technique to engineering problems are presented.
Author: Thomas Nall Eden Greville
Author: Thomas Nall Eden Greville
Author: I. J. Schoenberg
Author: Gary D. Knott
Author: 
Author: Ingrid Melinder
Author: University of Wisconsin--Madison. Department of Statistics
Author: I. J. Schoenberg
Author: Thomas Maindl
Author: James B. Cheek
Author: Mathematics Research Center (United States. Army)