Linear Systems: Direct and Iterative Methods

Related lectures (30)

Explores the Jacobi method and diagonalization techniques, including similarity transformation, power methods, and QR decomposition.

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Covers iterative methods for solving linear systems of equations and discusses the convergence properties of methods like Richardson's method.

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Explores the Cholesky factorization method for symmetric positive definite matrices.

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

Explores solving linear systems and addressing nonlinearity in numerical flow simulations using multigrid and linearization methods.

Covers the construction of an iterative method for linear systems, emphasizing matrix decomposition and convexity.

Explores the properties of invertible matrices, including unique solutions and linear independence.

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

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