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Basic and advanced linear algebra and numerical problems, numerical algorithms, and techniques with multiple applications in the field of Computer Science.

License: MIT License

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numerical-methods-for-computer-science's Introduction

Numerical-Methods-For-Computer-Science: Numerical Algorithms Implementation

This repository collects the implementation of numerical algorithms, with several applications in different field of artificial intelligence. This work has been developed during the Numerical Methods For Computer Science course @ Department of Computer Science @ University of Bari "Aldo Moro" under the supervision of dr. Francesca Mazzia and dr. Antonella Falini.

Numerical Algorithms Implementation & Applications

Matlab
- Numerical-Experiments
  - Floating Point Arithmetic Simulation with Chop Operation
  - Geometrical representations of ill-conditioned linear systems
  - Matrix Inverse, Involutory Matrix and Crypthography application
  - Eigenvalues, Eigenvectors and Spectral Clustering
Python
- Numerical-Experiments
  - Vectors and Matrices Operation
  - Gaussian Elimination with Floating Point Arithmetic & LU Decomposition
  - Echelon Form and Row Reduced Echelon Form with applications
    - Block Matrix Multiplication
    - Matrix Inverse
    - Computation of the spanning sets of all the four fundamental subspaces
    - Image compression
  - Matrix Product with applications
    - Airport, flights and connectivity matrix
  - Norms and Cosine similarity with applications
    - Linear Correlation
    - Text Mining using Vector-Space-model
  - Orthogonality
    - Standard and Modified Gram-Schmidt procedure
    - QR decomposition
    - QR with pivoting (rank-revealing algorithm) for image compression
    - QR with pivoting (rank-revealing algorithm) for text retrieval
  - Eigenvalues and Eigenvectors
    - Power Method and Normalized Power Method to compute the absolute dominant eigenvalue
    - Normalized Power Method for Google Page Rank
  - URV, SVD, PCA and Projector with applications
    - Image compression
    - Data reduction and visualization with Iris dataset
    - Face recognition with Yalenfaces dataset
    - Text retrieval (Principal compoenent regression)
  - Least-squares problem
- Numerical-Projects-Exam
  - PCA for digits recognition with mnist dataset
  - SVD for spectral clustering

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