Matrix Computations: Complexity and Algorithms

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (47)

Linear Systems: Direct Methods Log in to Mediaspace to watch this video

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Iterative Methods: Linear Systems Log in to Mediaspace to watch this video

Explores iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods, Cholesky factorization, and preconditioned conjugate gradient.

Singular Value Decomposition: Applications and Interpretation Log in to Mediaspace to watch this video

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Linear Systems: Direct and Iterative Methods Log in to Mediaspace to watch this video

Explores linear systems, covering direct and iterative methods for solving them with a focus on round-off errors and Richardson's algorithm.

Matrix Inversion: Basics and Properties Log in to Mediaspace to watch this video

Covers the basics of matrix inversion, properties of matrix multiplication, and the uniqueness of matrix inverses.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization Log in to Mediaspace to watch this video

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Matrix Multiplication: Applications and Properties Log in to Mediaspace to watch this video

Covers matrix multiplication, properties, and inverses in linear algebra.

Linear Systems: Triangular Matrices Log in to Mediaspace to watch this video

Focuses on transforming linear systems into triangular matrices to simplify the process of finding solutions.

Jacobi and Gauss-Seidel methods Log in to Mediaspace to watch this video

Explains the Jacobi and Gauss-Seidel methods for solving linear systems iteratively.

Richardson Method: Preconditioned Iterative Solvers Log in to Mediaspace to watch this video

Covers the Richardson method for solving linear systems with preconditioned iterative solvers and introduces the gradient method.

Linear Algebra: Inverse Matrix and Systems Resolution Log in to Mediaspace to watch this video

Covers the concept of inverse matrices and systems resolution, including the conditions for matrix invertibility and the Gauss-Jordan algorithm.

Matrix Arithmetic: Properties and Operations Log in to Mediaspace to watch this video

Explores matrix arithmetic, including properties, products, and dimensions, with a focus on matrix multiplication and commutativity.

Eigenvalues of Matrices: Properties and Relations Log in to Mediaspace to watch this video

Explores properties and relations of eigenvalues of square matrices and their products.

Matrix Operations: Partitions and Blocks Log in to Mediaspace to watch this video

Covers matrix operations, including partitioning and block multiplication.

Gaussian Elimination Method Log in to Mediaspace to watch this video

Explains the Gaussian elimination method for solving linear equations through row operations and pivoting.

Matrix Multiplication: Properties and Applications Log in to Mediaspace to watch this video

Explores matrix multiplication, its properties, and applications in linear maps.

Linear Algebra: Vector Spaces and Linear Independence Log in to Mediaspace to watch this video

Covers vector spaces, operations, and linear independence with examples from polynomials and functions.

Row Echelon Form: Gauss-Jordan Algorithm Log in to Mediaspace to watch this video

Covers row echelon forms and the Gauss-Jordan algorithm for solving linear systems.

Matrix Operations and Vector Spaces Log in to Mediaspace to watch this video

Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.

Least Squares Solutions Log in to Mediaspace to watch this video

Covers least squares solutions for linear systems using matrix operations and normal systems, illustrated with examples.

Page 2 of 3