DAMSL-091 Numerical Algorithms

Syllabus

• Floating point arithmetic,
• Stability of algorithms,
• Root finding algorithms: Bisection, Newton and Secant methods,
• Methods for solving linear systems: Direct methods (LU, Cholesky), Iterative methods (Jacobi, Gauss-Seidel, SOR, Steepest Descent, Conjugate Gradient),
• Singular Value Decomposition (SVD) and its applications,
• Least Squares problem,
• Interpolation and Numerical differentiation,
• Algorithms in Optimization,
• Monte Carlo methods.

Learning Outcomes

Upon completion of the course the students will be able to:

• Have good knowledge of the basic numerical algorithms in the field, their properties, and characteristics.
• Computer implementation of the algorithms
• Solution of basic applied problems using these algorithms
• Very good understanding of their capabilities, limitations, advantages, and disadvantages