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### Numerical methods in statistics - Laboratory

 Code: 61503 ECTS: 5.0 Lecturers in charge: izv. prof. dr. sc. Tina Bosner Lecturers: izv. prof. dr. sc. Tina Bosner - Exercises Daniela Ivanković , mag. math. - Exercises English level: 1,0,0 All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

### 1. komponenta

Lecture typeTotal
Lectures 15
Exercises 45
Description:
COURSE AIMS AND OBJECTIVES: introduce basic numerical methods used in statistics. The emphasis is in practical work in computer lab

COURSE DESCRIPTION AND SYLLABUS:
1. Direct methods for solving linear systems. Gaussian elimination, pivoting, LU decomposition, Cholesky decomposition.
2. Iterative methods for solving linear systems. Jacobi, Gauss-Seidel.
3. Least squares method. QR factorization, Householder's transformtions.
4. Least squares method. Givens rotations, conjugated gradient method.
5. Numerical solving of eigenvalue problems. Power method, QR decomposition, SVD.
6. Numerical solving of eigenvalue problems. Applications.
7. Function interpolation and approximation.
8. Discrete Fourier transformation.
9. Solving nonlinear equations. Bisection, secant method, Newton's method.
10. Solving nonlinear systems. Newton's method, Broyden's method.
11. Unconditional minimization. Newton's method. Secant method.
12. Nonlinear least square method.
13. Maximum likehood method.
14. Conditional minimization.
Literature:
1. J. F. Monaham: Numerical Methods of Statistics
2. J. E. Dennis Jr, R. B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations
3. A. Quarteroni, R. Sacco, F. Saleri: Numerical mathematics, Texts in Applied Mathematics, 37
 4. semester Mandatory course - Regular study - Mathematical Statistics
Consultations schedule: