Faculty of
Computer Science

• Examples, floating point computing, types of errors, propagation of errors
• LU decompositions (Gauss elimination algorithm, Cholesky factorisation), QR decompositiond (Givens and Householder algorithms), singular value decomposition
• Iterative methods for solving linear systems ( Jacobi and Gauss-Seidel methods, succesive overrealaxation)
• Eigenvalues and eigenvectors approximation (Jacobi method for symmetric matrices, QR type algorithms)
• Solving nonlinear equations and systems of nonlinear equations (Newton type methods, false position method, secant method, methods for the roots of polynomials)
• Polynomial interpolation (Lagrange polynomial, Newton polynomials), spline interpolation (linear continuous, cubic of class C2)
• Numerical integration (Newton-Cotes type formulae)

• Evaluation of elementary functions (sin/cos/...), errors in numerical computations;
• Solving linear systems:

1. Substitution method, LU decomposition;
2. QR decomposition: Givens or Householder algorithm;
3. Iterative methods: Jacobi and Gauss-Seidel methods;

• Jacobi method for finding the eigenvalues and eigenvectors for symmetric matrices;
• Solving nonlinear equations: bisection method, Newton-Raphson method,false position method, secant method, methods for approximating roots of polynomials;
• Polynomial interpolation: Newton-Lagrange polynomial, Aitken algorithm, C2 cubic spline functions;
• Numerical integration: Newton-Cotes type formulae, iterate methods.

• C. Ignat, C. Ilioi, T. Jucan, Elemente de informatică şi calcul numeric, Editura Univ. „Al.I. Cuza” Iaşi, 1989,
• T.A. Beu, Calcul numeric în C, Editura Albastră, Cluj, 2000,
• G. Dalquist, A. Bjorck, Numerical Methods, Prentice Hall, 1984,
• Numerical Recipes, http://www.nr.com/

Written exam