Numerical Linear Algebra: Least Squares, QR and SVD

TL;DR

This paper provides lecture notes on numerical linear algebra algorithms emphasizing least squares, QR, and SVD methods for overdetermined systems, with applications in data analysis.

Contribution

It offers a focused overview of algorithms like QR and SVD for solving overdetermined systems, distinct from traditional LU factorization methods.

Findings

Emphasizes least squares solutions for overdetermined systems.

Details orthogonal factorizations and their applications.

Provides practical insights into numerical algorithms in scientific computing.

Abstract

These lecture notes focus on some numerical linear algebra algorithms in scientific computing. We assume that students are familiar with elementary linear algebra concepts such as vector spaces, systems of equations, matrices, norms, eigenvalues, and eigenvectors. In the numerical part, we do not pursue Gaussian elimination and other LU factorization algorithms for square systems. Instead, we mainly focus on overdetermined systems, least squares solutions, orthogonal factorizations, and some applications to data analysis and other areas.