The course presents to students knowledge on basic numerical methods:
matrix operations, solving systems of linear algebraic equations and regression. Another part of the lecture deals with polynomial interpolation and solution of one-dimensional nonlinear equations.
After successful passing of the course the students should be able to
- list and describe basic numerical methods lectured
- successfully apply these methods for solving a specified problem.
1) Number representation in a computer,precision, accuracy.
Errors in numerical algorithms,
propagation of the errors.
Stability of the algorthims.
2) Systems of linear algebraic equations,
direct and iterative metods.
The Gauss elimination method, pivoting.
Systems with special matrices:
The Choleski theorem and the Choleski method, tridiagonal systems.
the Jacobi method,
the Gauss-Seidel method.
The problem of the convergence of the iteration methods.
3) Eigenvalues and eigenvectors of matrices.
The Householder transformation and the QR algorithm.
Iterative methods: the power method, convergence.
4) Singular value decomposition and its applications. Linear regression.