Course information for current students:
Important note on the use of bulletin boards:
No parts or whole of answers to the assignment problems
should be posted to the boards.
Any violation of this rule will bring trouble to the poster.
Please use judgement before posting.
MATLAB on cdf:
To use matlab on cdf, you need to login via ssh
(on an xterm in unix, linux, mac, or cygwin, and on putty in windows)
with a command such as
ssh -X user@cdf.toronto.eduwhere ``user'' is your cdf username, then, once on cdf, run
/usr/local/bin/matlabWithin matlab you may want to go to a certain directory, say ~/matlab, and for this you can use the unix shell command
cd ~/matlabwithin matlab. You may also want to have a starup.m file in that directory, to always run some standard commands (e.g. format compact) every time you start matlab.
Textbook web page (see educational modules)
Material already covered in the course (with textbook sections in parentheses)
9-1-2012 (2 hours)
0. What is Scientific Computing? (1.1, 1.2.1)
1. Computer arithmetic; data and computational errors
1.1 (Human) Representation of nonnegative integers
- Algorithm for converting base b integers to decimal
- Algorithm for converting decimal integers to base b
1.2 (Human) Representation of reals
- Algorithm for converting base b fractions to decimal
- Algorithm for converting decimal fractions to base b
1.3 Computer representation of numbers (1.3.1-7)
- floating-point numbers, mantissa, exponent, normalized mantissa,
significant digits, overflow, underflow, range of representable numbers,
representable numbers, chopping, rounding
- The IEEE Standard
1.4 Round-off error (1.3.5)
1.5 Absolute and relative errors (1.2.2)
1.6 Computer arithmetic (1.3.8)
1.7 Machine epsilon (1.3.5)
16-1-2012 (2 hours)
1.8 Error propagation in simple arithmetic calculations (1.3.8-9)
- Multiplication, division, addition/subtraction
- catastrophic cancellation
1.9 Error propagation in computation: conditioning of problems (1.2.6)
- condition number of function
1.10 Error propagation in computation: stability of algorithms (1.2.7)
1.11 Forward and backward errors (1.2.3-5)
Propagated data error
Truncation (discretization) and rounding errors, computational error
Total error
2. Direct methods for solving square linear systems
2.1 Vectors and matrices -- review of terminology
23-1-2012 (2 hours)
2.2 Solving lower triangular linear systems [2.4.2]
Forward substitution (f/s)
2.3 Solving upper triangular linear systems [2.4.2]
Back substitution (b/s)
2.4 Equivalent linear systems - row operations [2.4.1]
2.5 An example of solving a linear system by GE and b/s
2.6 Gaussian elimination (GE) [2.4.3, 2.4.4, 2.4.6-7]
2.7 LU factorization [2.4.3, 2.4.4, 2.4.7]
elementary Gauss (elimination) transformation matrices
-- symmetric and banded matrices skipped for later --
2.8 Computing the inverse of a matrix [2.4.7]
30-1-2012 (2 hours)
2.9 GE with partial pivoting [2.4.5-6]
breakdown or instability of GE, interchanges of rows, columns
types of pivoting
elementary Gauss transformation matrices; elementary permutation matrices
2.10 Scaled partial pivoting [2.4.10]
2.11 Complete pivoting
2.12 Symmetric and symmetric positive definite matrices [2.5.1, 2.5.2]
LDL^T and Choleski factorization
6-2-2012 (2 hours)
2.13 Banded matrices [2.5.3]
Banded LU/GE and b/f/s
2.14 MATLAB and solution of linear systems
2.15 Mathematical software [2.7]
2.16 Inner products
2.17 Norms [2.3]
2.18 Vector norms [2.3.1]
2.19 Matrix norms [2.3.2]
2.20 Condition number of a matrix [2.3.3-5]
To be done next:
Other interpretations of the condition number of a matrix
Notes and handouts:
Access to these data requires that
you type in your CDF username and last
4 digits of your student id.