Effect of Rounding Errors in Linear Systems

Related lectures (25)

Page 2 of 3

Explores floating point numbers, LU decomposition, errors in numerical computations, and the impact of round-off errors.

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

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

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.