COMPUTER SCIENCE 349A Handout Number 5 Taylor's Theorem is the fundamental tool for deriving and analyzing numerical approximation formulas in this course. It states that any "smooth" function (one with a sufficient number of derivatives) can be approxima
CSC349A Lecture Notes, September 17, 2015
Little, Rich
These are the lecture notes for CSC349A Numerical Analysis taught by
Rich Little in the Fall of 2015. They roughly correspond to the material covered in each lecture in the classroom but the actual cl
COMPUTER SCIENCE 349A
Handout Number 3
Two methods of representing a real number p in floating-point: rounding and chopping.
Example
Let b 10 , k 4 and p 2 / 3 .
floating - point
absolute error relative error
approximation to p
chopping
0.6666 10 0
0.000
1
Volume
UNIVERSITY OF VICTORIA
Department of Computer Science
MATLAB
User Manual
DEPARTMENT OF COMPUTER SCIENCE
MATLAB User Manual
Lanjing Li
Department of Computer Science
University of Victoria
PO Box 3055, STN CSC
Victoria, BC
Canada V8W 3P6
Table of
COMPUTER SCIENCE 349A
Handout Number 1
NUMERICAL ANALYSIS is the study of algorithms for solving problems of
continuous mathematics.
key words:
continuous mathematics
- means that real or complex
variables are involved
- the floating-point representation
CSC349A Numerical Analysis
Lecture 2
Rich Little
University of Victoria
2015
R. Little
1/7
Table of Contents I
1 MATLAB
2 Approximation and Roundoff Errors
R. Little
2/7
MATLAB
pgs. 27-39 - Elementary programming concepts and
pseudocode
pgs. 935-942 - App
COMPUTER SCIENCE 349A
Handout Number 4
SUBTRACTIVE CANCELLATION (pages 73-76 of the 6th edition; pages 76-79 of
the 7th edition)
Subtractive cancellation refers to the loss of significant digits during a floatingpoint computation due to the subtraction of
CSC349A Lecture Notes, September 14, 2015
Little, Rich
These are the lecture notes for CSC349A Numerical Analysis taught by
Rich Little in the Spring of 2015. They roughly correspond to the material
covered in each lecture in the classroom but the actual
CSC349A Numerical Analysis
Lecture 3
Rich Little
University of Victoria
2015
R. Little
1 / 16
Table of Contents I
1 Floating-point numbers
2 Floating-point arithmetic
3 Subtractive cancellation
R. Little
2 / 16
Floating-point number system
A floating-poin
W
f" (X0) 0‘ ' Xo )2
“IQ-fun) + f-(xuﬂx - x0) + +
ft”)(xo)(X-Xul“ f[n_l)(E(X])(X'Xo)("+n
+ n! +W
Where x0 5 Es x
PHCXJ —;fl{x) — RDCX] <- Tancation Error {remainder}
Determine second order (n=2) Taylor polynomial approx for
f(x) = x“4 expanded about xa