First Meeting: 16 January 2024
Class Timings: Tuesdays & Thursdays from 2:00 PM - 3:30 PM
Course Description:
Singular value decomposition for matrices and operators. Least-squares problems. Integral equations and inverse problems (deconvolution, denoising). Need for regularisation. L-curve, Cross-validation. Numerical methods: iterative, projection and Krylov-subspace. Beyond the 2-norm.
Reproducing kernel Hilbert spaces: definitions, properties and characterisation. Operations on kernels. Interpolation and approximation. Negative definite functions. Applications to machine learning. Mercer's theorem.
- Hansen. Discrete inverse problems: insight and algorithms Society for Industrial and Applied Mathematics 2010
- Paulsen and Raghupathi. An introduction to the theory of reproducing kernel Hilbert spaces Cambridge University Press 2016
- Trefethen and Bau. Numerical linear algebra Society for Industrial and Applied Mathematics 2022
- Homeworks 90 %
- Project 10 %
Prerequisites: Basic concepts from linear algebra. Familiarity with Python, R or similar langauges is assumed. Preferable: Functional analysis
- Teacher: Vishal Vasan