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.
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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
- Numerical-Experiments
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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
- Numerical-Experiments