Polska wersja

Computational Mathematics II



winter semester 2012-13

lecture Monday 1015-1145am room 4050 and classes/lab Monday 1215-145pm - blackboard classes in room 4050 or lab in room 2042 (MIMUW bdg., Banacha 2 - entrance - Pasteura Street)
Program of lab
please register to this course in USOS (computer system of University of Warsaw) - if 7 students are formally registered, then we will have classes (otherwise there will be only lecture)
Evaluation: an oral exam.
There may be computer labs (instead of standard "blackboard" classes)

The course is elementary - it is required to know the basics of liner algebra and calculus (mathematical analysis).

There are lecture notes for this course in Polish.
Evaluation will be based only on an oral exam.

Lecture notes

(In Polish) Piotr Krzyzanowski, Leszek Plaskota, Matematyka Obliczeniowa II, 2010.
Published on-line: WWW page (there is a link to pdf file with the lecture notes).

References

Text books

  1. James W. Demmel, Applied Numerical Linear Algebra. Society for Industrial and Applied Mathematics (SIAM), Philadelphia 1997.
  2. Peter Deuflhard, Andreas Hohmann. Numerical analysis in modern scientific computing, vol. 43 in Texts in Applied Mathematics. Springer-Verlag, New York, 2nd edition, 2003. An introduction.
  3. J.M. Jankowscy, M. Dryja. Przegląd metod i algorytmów numerycznych, tom I i II. Biblioteka inżynierii oprogramowania. Wydawnictwo Naukowo-Techniczne, Warszawa, 1995.
  4. C. T. Kelley. Iterative methods for linear and nonlinear equations, vol. 16 of Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1995 - covers iterative methods for linear equations (CG, PCG and GMRES), and solving nonlinear equations
  5. A. Kiełbasiński, H. Schwetlick. Numeryczna algebra liniowa. Wydawnictwa Naukowo-Techniczne, 1992.
  6. D.Kincaid, W.Cheney, Numerical Analysis, 2nd editione, Brooks/Cole, 1996. A general textbook for numerical methods.
  7. J. Stoer, R. Bulirsch. Introduction to numerical analysis. Translated from the German by R. Bartels, W. Gautschi and C. Witzgall. Third edition. Texts in Applied Mathematics, 12. Springer-Verlag, New York, 2002
  8. Lloyd N. Trefethen, David Bau, III, Numerical linear algebra. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1997.

Monographs or advanced text books

  1. John E. Dennis Jr., Robert B. Schnabel. Numerical methods for unconstrained optimization and nonlinear equations. Prentice-Hall Series in Computational Mathematics. Prentice-Hall Inc., En- glewood Cliffs, N.J., 1983.
  2. Peter Deuflhard. Newton methods for Nonlinear Problems. Affine Invariance and Adaptive Algori- thms. Springer International, 2002.
  3. Eugene G. Dyakonov. Optimization in solving elliptic problems. CRC Press, Boca Raton, FL, 1996. Translated from the 1989 Russian original, Translation edited and with a preface by Steve McCormick.
  4. Gene H. Golub, Charles F. Van Loan. Matrix computations. Johns Hopkins Studies in the Mathe- matical Sciences. Johns Hopkins University Press, Baltimore, MD, 3rd ed., 1996.
  5. J. M. Ortega, W. C. Rheinboldt. Iterative solutions of nonlinear equations in several variables. Academic Press, New York, 1970.
  6. Yousef Saad. Iterative methods for sparse linear systems. Society for Industrial and Applied Ma- thematics, Philadelphia, PA, 2nd ed., 2003. On-line
  7. Yousef Saad, Numerical Methods for Large Eigenvalue Problems. Society for Industrial and Applied Ma- thematics, Philadelphia, PA, 2nd ed., 2011. On-line
  8. A. A. Samarski, J. S. Nikołajew. Metody rozwiązywania równań siatkowych. PWN 1988.
  9. Barry F. Smith, Petter E. Bjorstad, William D. Gropp. Domain decomposition. Cambridge Univer- sity Press, Cambridge, 1996. Parallel multilevel methods for elliptic partial differential equations.
  10. Andrea Toselli, Olof Widlund. Domain decomposition methods - algorithms and theory, wolumen 34 serii Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 2005.
  11. J. F. Traub. Iterative Methods for the Solution of Equations. Englewood Cliffs, New York, 1964.

LAB

Some classes will be held in computer lab. Link to Octave (one can download linux or windows version of octave)
octave-forge - octave extension

octave manual in html

Program of labs and octave scripts with solution of some problems


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Last update: August 29th, 2012