Course Notes for
Introduction to Scientic Computation
Je Orchard, Lori Case
Winter 2016
David R. Cheriton School of Computer Science
University of Waterloo
September 24, 2015
1
Contributions to these notes have been made
by past and present instructors fo
Interpolation
More Flexible Curve Types
CS 370 - Lecture 8
May 18, 2016
Cubic splines via Hermite approach
Recall: we showed how to use Hermite interpolation ideas to solve for
a cubic spline.
1. Set up a linear system for slopes, by requiring matching 2
Interpolation
Bezier Curves
CS 370 - Lecture 9
May 20, 2016
1
Bezier Curves
This curve interpolates the end points. It is affected by the control
points, but doesnt interpolate them.
Control points
End points
The control points dictate the derivative at
CS370 Floating Point Error
CS370 - Floating point
1
Announcement: (Optional) MATLAB Tutorial
The tutorial will be offered by Ke Nian, one of your friendly
neighbourhood TAs.
Date: Tuesday, May 10
Time: 6-7pm
Location: MC 1056
CS370 - Floating point
2
Why
CS370 Numerical
Computation - Introduction
Term: Spring 2016
Instructor: Christopher Batty
Who am I?
CS Professor, part of the Scientific Computing (SciCom) group and
Computer Graphics Lab (CGL) here at Waterloo.
Former visual effects software engineer
Interpolation
Efficiently Computing Splines
CS370 Lecture 7
May 16, 2016
Two strategies for smooth curves
Hermite interpolation: Given points
and their slopes, fit a curve. Gives
matching 1st derivatives between
intervals.
Cubic spline interpolation: Giv
CS370 Lecture 1:
Floating Point Systems
CS370 - Floating Point
1
Topics
Floating Point Systems
Absolute and Relative Error
Cancellation and Round-off Errors
Conditioning of Problems
Stability of Algorithms
CS370 - Floating Point
2
Real numbers, , are
Inf
Interpolation Cubic Splines
CS370 May 13, 2016
Hermite interpolation Many points
Fit many points (given values and 1st deriv.) with piecewise Hermite interpolation?
Use one cubic per pair of (adjacent) points. The matching/shared derivative data at
points
Floating Point Error and
Stability
CS370 - May 6, 2016
CS370 - Floating point
1
Who are you?
1. What area(s) of CS are you most interested in?
2. What aspect/topic of the course are you most interested in?
3. What are your career plans/hopes for after gra
CS URA Program
Interpolation Piecewise
Polynomials and Cubic Splines
CS370 May 11, 2016
Lagrange polynomials: Line example
=
=1
1 1 +1 ( )( )
() , where =
1 1 +1 ( )( )
Consider the two points we fit a line to earlier:
(1 , 1 ) = 1,2 , (2 , 2 ) = 1,4
Unit 6:
Least Squares
How can we use many observations of a
phenomenon to infer a model?
Least Squares Page 1
L33: Least Squares
Goal: To see how the problem of least-squares crops up in data analysis.
Functional Magnetic Resonance Imaging (FMRI)
Function
Using matrix-vector notation
Hence, we get
Recall that
Fourier Page 13
Recall that
So
Notice that
Consider
Fourier Page 14
Recall the DFT is
This is the inverse DFT (IDFT). It takes Fourier coefficients, and converts
them to the spatial or temporal domain
Unit 1:
Floating-Point Numbers
How does the inaccuracy of computer arithmetic
affect the way we do computations?
Floating Point Page 1
L01: FP Problem
Goal: To see that computation on a computer can be inaccurate, even if
the math is correct.
Floating-Poi
Unit 5:
Numerical ODEs
Most Ordinary Differential Equations (ODEs) are not
solvable on paper. Here's how we deal with them
using computers.
ODEs Page 1
L27: Initial Value Problems
Goal: To learn a standard formulation for ordinary differential equations.
Unit 3:
Interpolation
Estimating what goes between samples.
Interpolation Page 1
L06: Introduction to Interpolation
Goal: To find out what interpolation is, and how it is useful.
Interpolation in Image Processing
A digital image is an array of pixels (pic
Computer Science 370: Numerical Computation (F14)
Floating Point Arithmetic
Topics:
Floating Point Systems
Absolute and Relative Error
Cancellation and Round-off Errors
Conditioning of Problems
Stability of Algorithms
CS370 - Floating Point
1
Floatin
Computer Science 370
Midterm Examination
Fall Term 2000
Date: October 25, 7:009:00 PM
This is an open book exam where all textbooks and notes are permitted. Do all questions
and show all work. The total marks available are 50.
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University of Waterloo
Department of Computer Science
CS370 Midterm Examination: Fall 2006
Thursday, November 2, 2006
Duration = 2 hours
Instructors: Y. Li
Name .
Student ID .
Section: 8:30 11:30
The aids allowed are:
- Printed Course Notes
- Lecture note
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CS 370 Spring 2016: Assignment 2
Due Monday, June 20, 4:00 PM.
Written/analytical work and all program outputs (figures, data, etc.) should be submitted as a
single PDF file to the Dropbox on LEARN. You can scan or photograph handwritten pages, or
typeset