Numerical Methods

  1. Eigenvalue Problems
    1. Problem Formulation
      1. Standard Eigenvalue Problem
        1. Generalized Eigenvalue Problem
          1. Properties of Eigenvalues
          2. Power Method
            1. Basic Power Method
              1. Algorithm
                1. Convergence Analysis
                  1. Dominant Eigenvalue
                  2. Inverse Power Method
                    1. Smallest Eigenvalue
                      1. Shifted Inverse Iteration
                        1. Convergence Acceleration
                        2. Deflation Techniques
                          1. Hotelling's Deflation
                            1. Wielandt's Deflation
                          2. QR Algorithm
                            1. QR Decomposition
                              1. Gram-Schmidt Process
                                1. Householder Reflections
                                  1. Givens Rotations
                                  2. Basic QR Algorithm
                                    1. Iteration Process
                                      1. Convergence Properties
                                      2. Practical QR Algorithm
                                        1. Hessenberg Form
                                          1. Implicit Shifts
                                            1. Deflation Strategies
                                          2. Jacobi Method
                                            1. Symmetric Matrices
                                              1. Jacobi Rotations
                                                1. Convergence Theory
                                                  1. Implementation Details
                                                  2. Lanczos Method
                                                    1. Krylov Subspaces
                                                      1. Tridiagonalization
                                                        1. Large Sparse Matrices
                                                          1. Reorthogonalization

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                                                        11. Optimization Methods

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                                                        1. Introduction to Numerical Methods