CSC336 Numerical Methods

Fall 2023 Bulletin board for csc336 Fall 2023 -- course outline -- MarkUs (not yet)

Course information for current students:

Textbook web page (see educational modules)

Material to be covered in the course (with textbook sections in parentheses)

2023-09-12 (3 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 -- saturation in addition (1.3.8)
1.7  Machine epsilon (1.3.5)
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
1.12 Taylor series
2023-09-19 (3 hours)
1.13 O(n^b) and O(h^a) notations

Tutorial on matlab
Tutorial on computer arithmetic

2023-09-26 (3 hours)
2.   Direct methods for solving square linear systems
2.1  Vectors and matrices -- review of terminology and properties
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
2.8  Symmetric and symmetric positive definite matrices [2.5.1, 2.5.2]
     LDL^T and Choleski factorizations
2023-10-02 (3 hours)
2.9  Banded matrices [2.5.3]
     Banded LU/GE and b/f/s
2.10 Computing the inverse of a matrix [2.4.7]
     Properties of inverse
     [more on elementary Gauss (elimination) transformation matrices]
Tutorial 3 (matrices, operation counts, GE/LU, inverse)

more to come

Notes and handouts:
Note on use of notes: Notes will be available when the course starts. While it may be convenient to study for the course by reading the notes, it should be made clear that the notes are not there to substitute the textbook or any relevant book. Notes are always more condensed and give less overall information than books.
Notes with math notation, etc, are difficult to read online. It may be preferable for some of you to print out the 4-page style notes on paper (preferably double-sided).

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Lecture notes

Tutorial notes Assignments Other