vallejos / fing-metnum

Numerical Methods, 2014 Final Project.

Final Projects for Numerical Methods, 2014, Fing

There are 2 folders for 2 different projects.

Obligatorio1_2014: Mathematical Modeling of Incentive Policies in P2P Systems

In order to stimulate cooperation among nodes in P2P systems, some form of incentive mechanism is necessary so as to encourage service contribution. Hence, designing and evaluating the stability, robustness and performance of incentive policies is extremely critical.

The paper with all the details for the model is included here: https://github.com/vallejos/fing-metnum/blob/master/Mathematical%20Modeling%20of%20Incentive%20Policies%20in%20P2P%20Systems.pdf

In part 1 of the implementation, the problem is expressed and solved using a Proportional Incentive Policy, for cooperators, reciprocators and defectors peers.

For part 2, a Image Incentive Policy is considered and the problem is solved using Euler Method and the Trapezoidal Rule.

[ZHAO2008] Zhao, Bridge Q. and Lui, John C.S. and Chiu, Dah-Ming. Mathematical Modeling of Incentive Policies in P2P Systems. Proceedings of the 3rd International Workshop on Economics of Networked Systems (NetEcon ’08), pp 97–102, ISBN 978-1-60558-179-8.

Obligatorio2_2014: Image Compression using SVD

In this project we use the SVD (Single Value Decomposition) to study the different compressions levels for an image.

The implemented algorithm is the Golub-Kahan-Reinsch Algorithm presented in [GOLUB2013] or [QUARTERONI2007]. A demonstration for the [GOLUB2013] algorithm is also included.

Finally, a few tests are run to reconstruct the image using different singular values in order to obtain the requested MSE quality.

[GOLUB2013] Golub, G.H. and Van Loan, C.F. Matrix Computations (4th edition). Johns Hopkins Studies in the Mathematical Sciences. ISBN 9781421407944. Johns Hopkins Univer- sity Press. 2013

[QUARTERONI2007] Quarteroni,A.andSacco,R.andSaleri,F.NumericalMathematics.ISBN9783540346586. Texts in Applied Mathematics. 2007