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Numerical Methods

Anul I, semestrul II

Course presentation

Course structure

Remarks

Curriculum

Course materials

Seminars

Test subjects

Course presentation
   The course of Numerical Methods is given for the students of the English stream of the Electrical Engineering and Computer Science branch of the Faculty of Engineering Taught in Modern Languages. The aim of this course is to introduce the students to the specific of numerical computation, especially in basic linear algebra problems. The topics discussed will be matrix multiplication, solution of linear systems of equations, iterative methods for linear systems, linear least squares problems, the computation of eigenvalues and eigenvectors.
   Computation with real numbers represented in the floating point format has some particularities that makes it a nontrivial task. In addition to the efficiency (in terms of execution time and used memory) of an algorithm, the programmer should be concerned also with the limitation of the inherent errors in numerical computation. The Numerical Methods course presents, for each algorithm discussed, the reasons that lie behind its reliability and efficiency. Thus, the student will accumulate the know-how of designing and evaluating numerical algorithms.
   The students are expected to have followed and understood the course of Linear Algebra. They should also be familiar with a programming language.
Course structure
  • Faculty of Engineering Taught in Modern Languages
  • Branch: Electrical Engineering and Computer Science
  • 1st year, 2nd semester
  • Credit points: 4 (?)
  • Activities:
course: 28 hours (2 hours/week)
seminar: 28 hours (2 hours/week)
total: 56 hours
  • Instructor:
conf.dr.ing. Bogdan Dumitrescu
  • Required previous courses: Linear Algebra, Programming
  • How the final marks are computed:
start bonus: 10 points
seminar attendance: 10 points
seminar activity: 20 points
homeworks: 10 points
final test: 50 points
total: 100 points
   The seminar attendance will be appreciated as follows: for 10 or more seminars attended, the student receives 10 points; for 9 seminars attended, 9 points etc.
   The activity at the seminar will be appreciated upon the number of problems solved at the blackboard. Also, there will be small tests in each all students will receive the task of solving independently a problem.
   The homeworks consist of solving problems given at the seminars and not solved there.
   The final test will take 100 minutes and will consist of solving 3-4 problems. The students will be allowed to use any written material. However, the use of any computing device is forbidden. The minimum number of points required to pass the test is 15.
   The final mark will be computed by summing the points for the above activities, dividing by 10 and rounding.
Remarks
   During the final test, the exchange of any oral or written information between students is forbidden. The instructor reserves the right of punishing both the provider and the receiver of information. The punishment consists of cancellation of the test for the students involved in the exchange and may come during or after the test.
Curriculum
1. Introduction. The floating point format. Conditioning of numerical problems. Stability of numerical algorithms. 4 hours
2. Direct methods for solving linear systems. Gaussian elimination. The LU factorization. The Cholesky factorization. The determinant and the inverse of a matrix. 8 hours
3. Iterative methods for solving linear systems. 2 hours
4. The linear least squares problem. Orthogonal transformations, reflectors and rotations. Orthogonal triangularization. The QR factorization. Solution of over and underdetermined linear systems. 6 hours
5. Eigenvalues and eigenvectors. The power and inverse power methods. The QR method. 4 hours
6. The singular value decomposition and its applications. 2 hours
Seminars
 
   The purpose of seminars is to solve problems that review and complete the information given at the course. The problems will be solved mainly by the students. (The instructor has no intention of transforming the seminars into courses.) The students are free to propose any correct solutions to the given problems and are encouraged to volunteer for presenting their solutions at the blackboard. Also, the students are welcome to propose problems related to the course topic.
Test subjects
 
   Exemples of problems given at the final test are given in the download section of this site.