B38EI2/amc
HERIOT-WATT UNIVERSITY DEPARTMENT OF COMPUTING & ELECTRICAL ENGINEERING
Electrical Circuits and Machines Revision Tutorial Hughes Electrical Technology - Chapter 4
1. A network is arranged as shown in Fig. Calculate the value of the current in
Chapter 05.10
Shortest Path of a Robot
After reading this chapter, you should be able to:
1. find the shortest smooth path through consecutive points, and
2. compare the lengths of different paths.
Example
Peter: Dr. Kaw, I am taking a course in manufactu
A Note On Cubic Splines, AMATH 352, March 4, 2002
We would like to use a spline to approximate a function represented by the points 0 0 1 0 3 2
and 4 2 . The rst task is to determine the spacing between the points h k , the slopes dk and then
(though the
CHAPTER 5
Spline Approximation of Functions
and Data
This chapter introduces a number of methods for obtaining spline approximations to given
functions, or more precisely, to data obtained by sampling a function. In Section 5.1, we
focus on local methods
Splines
Let a = x0 < x1 < . . . < xn1 < xn = b. A spline of degree m is a function
S(x) which satises the following conditions:
1. For x [xi , xi+1 ], S(x) = Si (x): polynomial of degree m
2. S (m1) exists and continuous at the interior points x1 , . . .
Introduction to Numerical Analysis
Doron Levy
Department of Mathematics
and
Center for Scientic Computation and Mathematical Modeling (CSCAMM)
University of Maryland
September 21, 2010
D. Levy
Preface
i
D. Levy
CONTENTS
Contents
Preface
i
1 Introduction
1
Spline Functions An Elegant View of Interpolation
Bruce Cohen
bic@cgl.ucsf.edu
http:/www.cgl.ucsf.edu/home/bic
David Sklar
dsklar46@yahoo.com
Start with xv intensity controls
Some Goals
To present a concrete introduction to a widely used class of
methods
Cubic Spline Interpolation
Sky McKinley and Megan Levine
Math 45: Linear Algebra
Abstract. An introduction into the theory and application of cubic splines with accompanying Matlab
m-file cspline.m
Introduction
Real world numerical data is usually difficu
Basis Basics
Selected from presentations by
Jim Ramsay, McGill University,
Hongliang Fei, and Brian Quanz
1. Introduction
Basis: In Linear Algebra, a basis is a
set of vectors satisfying:
Linear combination of the basis can
represent every vector in a giv
Lecture 19
Polynomial and Spline Interpolation
A Chemical Reaction
In a chemical reaction the concentration level y of the product at time t was measured every half hour. The
following results were found:
t 0 .5 1.0 1.5 2.0
y 0 .19 .26 .29 .31
We can inpu
Unit 5: Cubic Splines
Let K = cfw_x0, . . . , xm be a set of given knots with
a = x0 < x1 < < xm = b
Denition. [11.2] A function s C 2[a, b] is called a cubic spline on [a, b],
if s is a cubic polynomial si in each interval [xi, xi+1].
It is called a cubi
Math 128A Spring 2002
Sergey Fomel
Handout # 17
March 14, 2002
Answers to Homework 6: Interpolation: Spline Interpolation
1. In class, we interpolated the function f (x) =
satised the natural boundary conditions
1
x
at the points x = 2, 4, 5 with the cubi
Cubic Spline Interpolation
Introduction
In the last lecture we saw that linear splines are a cheap way to interpolate our n + 1 points (x 0 , y0 ) to
(xn , yn ).
In general, the linear spline function is not continuously dierentiable. Its slope changes ab
CUBIC SPLINE INTERPOLATION: A REVIEW
George Walberg
Department of Computer Science
Columbia University
New York, NY 10027
wolberg@cs.columbia.edu
September 1988
Technical Repon CUCS-389-88
ABSTRACT
The purpose of this paper is to review the fundamentals o
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Page 810
CHAP. 19
Numerics in General
Spline Interpolation
Given data (function values, points in the xy-plane) (x0, 0), (x1, 1), , (xn, n) can be
interpolated by a polynomial Pn(x) of degree n or less so that the curve
CUBIC SPLINE INTERPOLATION: A REVIEW
George Walberg
Department of Computer Science
Columbia University
New York, NY 10027
wolberg@cs.columbia.edu
September 1988
Technical Repon CUCS-389-88
ABSTRACT
The purpose of this paper is to review the fundamentals o
Natural Cubic Interpolation
Jingjing Huang
10/24/2012
Interpolation
Construct a function crosses known points
Predict the value of unknown points
Interpolation in modeling
3
Interpolation
Polynomial Interpolation
Same polynomial for all points
Vander
SPLINE INTERPOLATION
Spline Background
Problem: high degree interpolating polynomials often
have extra oscillations.
1
Example: Runge function f (x) = 1+4x2 , x [1, 1].
1/(1+4x2) and P8(x) and P16(x)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1
0.8
0.6
0.4
0.
.
Spline interpolation
Given a tabulated function fk = f(xk ), k = , . . . N, a spline is a polynomial between each pair of tabulated
points, but one whose coefficients are determined slightly non-locally. The non-locality is designed to
guarantee global
Lecture 9 Cubic Spline Examples
9
Cubic Spline Examples
9.1
Mon 08/02/10
22
Solution:
From (8.12) we see we are looking for S(x)=
Recall.
During Wednesdays lecture we saw that each cubic in
the spline interpolant can be written as
si (x) = i (x xi1 ) + i
Mechanical Engineering in Context 1
ENERGY/PROJECTILE
Name: Ahmed Gouda
Registration No.: H00231949
Username:asg6
Subject Name and code: Mechanical in engineering in context 1
Supervisor: Mounif, Abdallah
Briefly summarise in your own words the purpose of