# Spline approximation as applied to aeronautical problems

by P. Ramamoorthy

Publisher: National Aeronautical Laboratory in Bangalore

Written in English

## Subjects:

• Airplanes -- Wings -- Testing,
• Spline theory,
• Pressure

## Edition Notes

Bibliography: p. 5.

Classifications The Physical Object Statement by P. Ramamoorthy & C. L. Narayana. Series NAL Technical note, TN-20 Contributions Narayana, C. L., joint author. LC Classifications TL504 .B35 TN-20, TL574.P7 .B35 TN-20 Pagination i, 5 p. Open Library OL27638M LC Control Number sa 68019765

Search the world's most comprehensive index of full-text books. My library. XLS Solver applied to solution of equations, interpolation, and approximation Acurveﬁtting example where using Excel Trendline gave poor results Different problems solved by different methods Use of cubic splines for interpolation Contains the spline functions necessary for the previous File Size: KB.   This video looks at an example of how we can interpolate using cubic splines, both the Natural and clamped boundary conditions are considered. Text Book: Numerical Analysis by Burden, Faires & Burden. One of the simplest methods is linear interpolation (sometimes known as lerp). Consider the above example of estimating f().Since is midway between 2 and 3, it is reasonable to take f() midway between f(2) = and f(3) = , which yields Generally, linear interpolation takes two data points, say (x a,y a) and (x b,y b), and the interpolant is given by.

Schoenberg, Contributions to the problem of approximation of equidistant data by analytic functions, Math., vol. 4, pp. 45–99 and –, External links. O'Connor, John J.; Robertson, Edmund F., "Isaac Jacob Schoenberg", MacTutor History of Mathematics archive, University of St Andrews. Isaac Jacob Schoenberg at the Mathematics Genealogy Project. This is a Wikipedia book, a collection of Wikipedia articles that can be easily saved, imported by an external electronic rendering service, and ordered as a printed book. Edit this book: Book Creator Wikitext. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the by: Get this from a library! Multivariate splines. [C K Chui; Society for Industrial and Applied Mathematics.] -- The subject of multivariate splines has become a rapidly growing field of mathematical research. The author presents the subject from an elementary point of view that parallels the theory and.

In this paper, Generalized Burgers-Fisher Equation(GBFE) is fully-integrated by using exponential cubic B-Spline collocation method in space and Crank Nicolson method in time. The numerical results are given to illustrate the efficiency of the proposed method and compared with both the exact solutions and some earlier is shown that accuracy is increased with an Cited by: 9. ECE ECE Problem Solving I Chapter 6: Problem Solving Applied: Rise-Time and Fall-Time Determination 6–11 Problem Solving Applied: Rise-Time and Fall-Time Determination In the design of electronic devices/circuits/systems that process pulse type signals, we are often interested in a performance char-acterization known as rise-time/fall-time. Get this from a library! Lectures on constructive approximation: fourier, spline, and wavelet methods on the real line, the sphere, and the ball. [Volker Michel] -- Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical. The box spline can be interpreted as the shadow of the indicator function of the unit hypercube in when projected down this view, the vectors ∈ are the geometric projection of the standard basis in (i.e., the edges of the hypercube) to.. Considering tempered distributions a box spline associated with a single direction vector is a Dirac-like generalized function supported on for ≤.

## Spline approximation as applied to aeronautical problems by P. Ramamoorthy Download PDF EPUB FB2

This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters.

The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar by: In some problems of Aeronautics such as the analysis of pressure data obtained from the wind tunnel testing on wing models or the determination of tie boundary layer characteristics from a known pressure distribution on an aerofoil one encounters with the interpolation, differentiation and integration of a functvon (eg.

pressure) given at unequal : P Ramamoorthy and CL Narayana. Book Description. The latest edition of this classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines.

It includes a supplement outlining the major advances in the theory sinceand some new references. Ideal for courses in splines, approximation theory or numerical by: A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.

Approximation and Modeling with B-Splines is appropriate as an advanced undergraduate or first-year graduate text for courses on splines or approximation and geometric modeling for students in mathematics, engineering, and.

Using the B-spline representation for splines, and separating the linear and nonlinear aspects, the approximation problem reduces to nonlinear least squares in the variable knots. We describe the problems encountered in this formulation caused by the “lethargy” theorem, and how a logarithmic transformation of the knots can lead to an effective method for computing free knot spline by: Answer h (based on the estimate for the Taylor remainder) 1 Polynomials 7 Problem Cubic Taylor Approximation of a Di erential Equation Approximate the solution y(x) of the initial value problem y0= 3x+ 2=y; y(0) = 1; at x= 1=10 with the aid of a cubic Taylor Size: KB.

Spline function approximation for differential equations Computer Methods in Applied Mechanics and Engineering, Vol. 26, No. 2 Numerical simulation of external and internal gasdynamic problemsCited by: Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets.

18 Solving Applied Mathematical Problems with MATLAB uct of matrices Aand B, such that cij= aijbij. The dot product is also referred to as the Hadamard product. Dot operation plays an. The book will greatly interest only advanced researchers and specialists in applied mathematics for CAD research.

“Development of Algorithms,” defines the theoretical framework for the algorithms discussed throughout the book, and its sections cover spline approximation and smoothing, spline interpolation and shape preservation. For the specific growth rate estimation via cubic smoothing spline, the MATLAB function csaps (x,y,p) was applied with x the total time of the process, the total cell mass y, and the chosen value for the fitting parameter p.

This function is an implementation of the. An important example is the solution of moment problems via rational approximation. Best quadrature formulae or the search for best linear spaces often leads to the consideration of spline functions with free nodes.

The most famous problem of this kind, namely best interpolation by poly­ nomials, is treated in the appendix of this : Springer-Verlag Berlin Heidelberg.

Computer Methods in Applied Mechanics and Engineering, Vol. No. A NUMERICAL SIMULATION OF FLUID–STRUCTURE INTERACTION IN INTERNAL FLOWS Numerical Heat Transfer, Part B: Fundamentals, Vol.

47, No. 5Cited by: Using this Guide (p. ) Outlines the organization of this user’s guide. Splines in MATLAB (p. ) Compares spline approximation using the MATLAB® spline command with the capabilities of the Spline Toolbox.

Expected Background (p. ) File Size: 6MB. Solving Applied Mathematical Problems with MATLAB. Solving Applied Mathematical Problems with MATLAB book. By Dingyü Xue, YangQuan Chen. Edition 1st Edition.

First Published eBook Published 3 November Pub. location New York. Data Interpolation and Functional Approximation Problems. This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters.

The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections.

Gopi M and Manohar S () A Unified Architecture for the Computation of B-Spline Curves and Surfaces, IEEE Transactions on Parallel and Distributed Systems,(), Online publication date: 1-Dec Spline approximation, using both values y i and x i as observations, is of vital importance for engineering geodesy, e.g., for approximation of profiles measured with terrestrial laser scanners, because it enables the consideration of arbitrary dispersion matrices for the : Frank Neitzel, Nikolaj Ezhov, Svetozar Petrovic.

The cubic spline u(x) satisfying conditions () is called interpolation spline with data {c j } j. The data set is assumed to coincide with the knot set {x j }. Since the number of conditions in () is N, we see that there remain (N + 2) – N = 2 free parameters. Book Description.

Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering.

Knot insertion algorithms are change of basis procedures for B-spline curves. Given the B-spline coefficients of a spline curve with respect to a knot vector {t k }, a knot insertion procedure finds the B-spline coefficients of the same spline curve with respect to another knot vector {u j } ⊃ {t k}.

The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal.

Focussing on key algorithms for computing with bivariate splines on triangulations in the plane and on the sphere, this book illustrates the usefulness of splines in solving problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of Range: \$ - \$ In mathematics, a spline is a special function defined piecewise by polynomials.

In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.

Cubic Spline Interpolation Cubic Spline Approximation: Problem:Givenn 1 pairs of data points xi, yi, i 0,1,n, find a piecewise-cubic polynomial S x S x S0 x a0 b0 x −xi c0 x −x0 2 d 0 x −x0 3 if x 0 ≤x ≤x1 S1 x a1 b1 x −x1 c1 x −x1 2 d 1 x −x1 3 if x 1 ≤x ≤x2 Sn−1 x an−1 bn−1 x −xn−1 cn−1 x −xn−1File Size: KB.

[2] has considered the applications of cubic spline functions for the solution of two point boundary value problems. Some of the books which discuss splines include Ahlberget et al.[3], deBoor [4], Prenter[5], Schumaker [6], Shikin and Plis [7] and Spath [8].

Chawla and Katti [9] employed nite di erence method for a class of singular two point. “The purpose of this book is to thoroughly prepare the reader for a research in spline and spline wavelet methods to signal and image processing theory at an advance level.

The book is a textbook for graduate students and one of the major consulting reference for the researcher in the field of spline wavelet theory and image processing. A new metamodel-assisted sampling search approach applied to the aerodynamic shape optimization of turbomachinery airfoils is presented in this paper.

The proposed methodology integrates a non-uniform rational B-spline (NURBS) geometry representation, a twodimensional flow analysis, and an improved metamodel driven Cited by: 2. Approximation with Active B-spline Curves and Surfaces Helmut Pottmann, Stefan Leopoldseder, Michael Hofer Institute of Geometry Vienna University of Technology Wiedner Hauptstr.

8–10, Vienna, Austria pottmann,leopoldseder,hofer @ Abstract An active contour model for parametric curve and sur-face approximation is presented.

The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for nonlinear weighted least squares (NWLS) approximation are restricted to a bounded definition range.

We present an algorithm termed nonlinear recursive B-spline approximation (NRBA) for an iterative NWLS approximation of an unbounded set Cited by: 1. It is well known that the quartic B-spline has been widely applied for the approximation solution of boundary value problems. Caglar used quartic B-spline to solve the linear cubic order boundary value problem.

Besides, quartic B-spline was also used to solve fifth order boundary value problems and the obstacle problems [24, 25]. Our method is Cited by: 3.A B-spline basis for natural splines was introduced in [7] and was later used in [14] to compute smoothing splines.

See also [22]. An extensive treatment of natural splines can be found in .This book is ideal as an advanced undergraduate or first-year graduate text for courses on splines or approximation and geometric modeling for students in mathematics, engineering and computer science. A supplementary web site provides a collection of problems with selected solutions, slides for use in lectures, and programs with demos.