Error Analysis: Discrete FD Scheme

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Explores computational methods in quantum physics, emphasizing exact diagonalization and space discretization techniques.

Covers direct methods for solving linear systems in numerical analysis.

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

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

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

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

Explores linear combinations, matrix-vector product, and matrix equation solutions.

Covers LU factorization, linear independence, and matrix equations.

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

Examines conditions for the existence of invertible matrices satisfying specific matrix equations involving eigenvalues.