Class schedule

Date Topics
Tu 1/12 Number systems and formats.
Th 1/14 Floating point numbers. Basic operations. Absolute and relative error.
Tu 1/19 Error propagation. Cancellation and loss of precision.
Th 1/21 Simple iterations. Lagrange's theorem on Taylor series. Trigonometric functions. π.
Tu 1/26 Logarithms. Roundoff error analysis of Taylor series.
Th 1/28 Pairwise summation. Euler transform. Aitken extrapolation.
Tu 2/2 Conditioning. Backward error analysis.
Th 2/4 Backward stability. Stability. Accuracy.
Tu 2/9 Gaussian elimination. LU decomposition.
Th 2/11 Backward stability of LU decomposition. Conditioning of linear systems.
Tu 2/16 Gram-Schmidt orthogonalization. QR decomposition.
Th 2/18 Least squares. Householder reflection and Givens rotation.
Tu 2/23 Lagrange interpolation. Lagrange coefficients. Pointwise error estimate.
Th 2/25 Midterm exam
2/29–3/4 Reading week
Tu 3/8 Lebesgue constants for Lagrange interpolation. Numerical differentiation.
Th 3/10 Uniform approximation. Weierstrass approximation theorem. Bernstein polynomials.
Tu 3/15 De la Vallée Poussin's theorem. Chebyshev's equioscillation theorem.
Th 3/17 Chebyshev polynomials. Lagrange interpolation with Chebyshev nodes.
Tu 3/22 Least squares approximation. Legendre polynomials.
Th 3/24 Lebesgue constants for Chebyshev truncation. Simple quadrature rules.
Tu 3/29 Newton-Cotes quadrature. Euler-Maclaurin formula.
Th 3/31 Bernoulli numbers. Romberg integration.
Tu 4/5 Gauss quadrature. Improper integrals.
Th 4/7 Fixed point iterations. Newton-Raphson method. Multiple roots.
Tu 4/12 Bisection. Secant method. Regula Falsi.
Th 4/14 Newton's method. Gradient descent. Line search.
Fr 4/22 Final exam (2pm, Currie Gym)

Reference books

Online resources

Course outline

Instructor: Dr. Gantumur Tsogtgerel

Prerequisite: MATH 325 (Honours ODE) or MATH 315 (ODE), COMP 202 or permission of instructor.

Corequisite: MATH 255 (Honours Analysis 2) or MATH 243 (Analysis 2).

Restriction: Intended primarily for Honours students.

Calendar description: Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

Topics to be covered:

Homework: We will have 3–4 homework assignments. Each assignments will consist of theoretical and programming components.

Exams: A midterm exam and a final exam. Each exam will consist of a theory exam in class, and a programming ("lab") exam to be done at home.

Grading: Homework 30%, Midterm 20%, Final 50%.

Midterm exam

The following topics will be covered.

Final exam

The final course grade will be computed as Homework 30% + MAX{ Final 70% , Final 50% + Midterm 20% }