Lectures related to Sparse matrix

Covers the solution of linear systems using direct methods and the evolution of matrices.

Matrix Construction and Function Manipulation

Covers tips on matrix construction and function manipulation using MATLAB.

Finite Difference Methods: Linear Systems and Band Matrices

Covers the application of finite difference methods to solve partial differential equations.

Conjugate Gradient Method: Solving Linear Systems

Covers the Conjugate Gradient method for solving linear systems without pre-conditioning, exploring parallel computing implementations and performance predictions.

Direct Methods for Solving Linear Equations

Explores direct methods for solving linear equations, LU factorization, Gass elimination, and computational complexity.

Linear Systems: Direct Methods

Explores linear systems, Gaussian elimination, LU decomposition, and matrix types.

Computational Quantum Physics

Covers exact diagonalization methods for many-particle systems in quantum physics.

Uncertainty Principle

Explores the uncertainty principle in quantum mechanics, covering compatible observables, system states, and mathematical representations of uncertainty.

Eigen Library for Linear Algebra

Explores the Eigen library for linear algebra, covering vectors, matrices, arrays, memory management, reshaping, and per-component operations.

Normal Ordered Product And Wick Theorem

Covers normal ordered product, Wick's theorem, creation and destruction fields, and efficient computation methodology.

Binary Spiked Matrix Estimation

Explores binary spiked matrix estimation, analyzing consistent equations and Bayesian estimators.

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Matrix Computations: Low Rank Approximation

Explores the complexity of matrix computations, focusing on low rank approximation algorithms and their applications.

Fourier Transform: Basics and Applications

Covers the basics of Fourier transform and the significance of fixed angular momentum states in mass calculations.

QR Factorization

Explains the QR factorization theorem and demonstrates the Gram-Schmidt procedure with an example.

Quantum Physics I

Explores eigenvalues, ladder operations, and quantum number values in quantum physics.

Modern Regression: Smoothing and Modelling Choices

Explores roughness penalty, band matrices, and Bayesian inference in regression smoothing.

Numerical Flow Simulation: Methods and Applications

Explores numerical methods for flow simulation, including finite element, spectral, particle, and lattice Boltzmann methods.

Optimal Distributed Control: Projected GD for Locally Optimal Controllers

Covers optimal distributed control using Gradient Descent to achieve locally optimal controllers in large-scale systems.

Correlation Functions & Spectra

Covers correlation functions, Franck-Condon transitions, Born-Oppenheimer approximation, and spectra.