📓 CME 302

        • Drawing 2023-10-04 2.excalidraw
        • Drawing 2023-10-04 12.13.49.excalidraw
        • Drawing 2023-10-04 12.26.03.excalidraw
        • Drawing 2023-10-15 18.35.05.excalidraw
        • Drawing 2023-10-15 18.36.19.excalidraw
        • Drawing 2023-10-18 11.37.23.excalidraw
        • GMRES least-squares problem 2023-11-29 10.49.27.excalidraw
        • Gram-Schmidt 2023-10-15 17.54.00.excalidraw
        • Least-squares solution using SVD 2023-10-15 20.28.15.excalidraw
        • MINRES 2023-12-04 08.40.09.excalidraw
        • QR iteration with shift 2023-10-30 11.49.00.excalidraw
        • QR using Givens transformations 2023-10-18 11.41.30.excalidraw
        • QR using Householder transformations 2023-10-18 11.37.36.excalidraw
      • 2024 complete and painless Conjugate Gradient
      • Accelerating convergence using a shift
      • Algorithm for QR iteration with shift
      • Algorithm for the Arnoldi process
      • Algorithm for the Lanczos process
      • All the orthogonality relations in CG
      • Angle between subspaces
      • Applying a Householder transformation
      • Arnoldi process
      • Backward error analysis for LU
      • Bootcamp
      • Brief introduction to Conjugate Gradients
      • Cauchy-Schwarz
      • CG search directions
      • Chebyshev iteration
      • Cholesky factorization
      • Classical iterative methods to solve sparse linear systems
      • Computational cost of Arnoldi and Lanczos
      • Computationally efficient search directions
      • Computing eigenvalues
      • Computing eigenvectors using the Schur decomposition
      • Computing multiple eigenvalues
      • Conditioning of a linear system
      • Conjugate Gradients algorithm
      • Conjugate Gradients code
      • Conjugate Gradients Version 1
      • Connection between Arnoldi and polynomials of A
      • Connection between Krylov subspace and Arnoldi
      • Convergence of classical iterative methods
      • Convergence of GMRES
      • Convergence of Lanczos eigenvalues for symmetric matrices
      • Convergence of Lanczos inner eigenvalues
      • Convergence of the Conjugate Gradients
      • Convergence of the orthogonal iteration
      • Convergence with conjugate steps
      • Deflation in the QR iteration
      • Determinant
      • Diagonalizable matrices
      • Dot product
      • Eigenvalues
      • Eigenvalues cannot be computed exactly
      • Exact shift
      • Existence of LU
      • Existence of the Cholesky factorization
      • Flexible preconditioned conjugate gradient method
      • Floating point arithmetic and unit roundoff error
      • Floating point arithmetic is different from regular arithmetic
      • Floating point numbers
      • Forward and backward error
      • Gauss-Seidel iteration
      • Ghost eigenvalues in the Lanczos process
      • GMRES
      • GMRES algorithm
      • GMRES least-squares problem
      • Gram-Schmidt
      • Hermitian and symmetric matrices
      • Householder transformation
      • Invertible matrix
      • Iterative methods for eigenvalue computation
      • Jacobi iteration
      • Key idea of iterative methods for eigenvalue computation
      • Krylov iterative methods to solve sparse linear systems
      • Krylov methods for sparse systems
      • Krylov subspace
      • Lanczos process
      • Least-squares problems
      • Least-squares solution using QR
      • Least-squares solution using SVD
      • LU algorithm
      • LU and determinant
      • Matrix block operations
      • Matrix-vector and matrix-matrix product
      • Method of normal equation
      • Method of power iteration
      • MINRES
      • Motivation of iterative methods for eigenvalue computation
      • Operator and matrix norms
      • Optimal step size
      • Orthogonal iteration
      • Orthogonal iteration algorithm
      • Orthogonal matrix and projector
      • Outer form of matrix-matrix product
      • Preconditioned Conjugate Gradients algorithm
      • Preconditioned Conjugate Gradients code
      • Preconditioning
      • Preconditioning the Conjugate Gradients algorithm
      • Projection
      • Pythagorean theorem
      • QR factorization
      • QR factorization and least-squares
      • QR iteration
      • QR iteration 2x2 example
      • QR iteration for upper Hessenberg matrices
      • QR iteration with shift
      • QR using Givens transformations
      • QR using Householder transformations
      • Rajat's painless Conjugate Gradients
      • Residuals and solution increments in CG
      • Row pivoting
      • Schur decomposition
      • Sensitivity analysis
      • Sherman-Morrison-Woodbury formula
      • Singular value decomposition
      • Solving linear systems
      • Solving linear systems using LU
      • Solving triangular systems
      • Some orthogonality relations in CG
      • SOR iteration
      • SOR iteration as a splitting method
      • Space and time costs of CG and GMRES
      • Splitting methods
      • Stability of the Cholesky factorization
      • Stability of the LU factorization
      • Subspace and linear independence
      • Summary of convergence and cost of the QR iteration
      • Summary of least-squares solution methods
      • Symmetric and unsymmetric QR iteration
      • Symmetric Positive Definite Matrices
      • The four fundamental spaces
      • Three-term recurrence
      • Trace
      • Triangular factorization
      • Uniqueness of the QR factorization
      • Unitarily diagonalizable matrices
      • Upper Hessenberg form for the QR iteration
      • Vector norms
      • Vectors and matrices
      • Why eigenvalues
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    Excalidraw

    Folder: Excalidraw

    13 items under this folder.

    • Dec 05, 2024

      Drawing 2023-10-18 11.37.23.excalidraw

      • excalidraw
    • Dec 05, 2024

      GMRES least-squares problem 2023-11-29 10.49.27.excalidraw

      • excalidraw
    • Dec 05, 2024

      Gram-Schmidt 2023-10-15 17.54.00.excalidraw

      • excalidraw
    • Dec 05, 2024

      Least-squares solution using SVD 2023-10-15 20.28.15.excalidraw

      • excalidraw
    • Dec 05, 2024

      MINRES 2023-12-04 08.40.09.excalidraw

      • excalidraw
    • Dec 05, 2024

      QR iteration with shift 2023-10-30 11.49.00.excalidraw

      • excalidraw
    • Dec 05, 2024

      QR using Givens transformations 2023-10-18 11.41.30.excalidraw

      • excalidraw
    • Dec 05, 2024

      QR using Householder transformations 2023-10-18 11.37.36.excalidraw

      • excalidraw
    • Dec 05, 2024

      Drawing 2023-10-04 12.13.49.excalidraw

      • excalidraw
    • Dec 05, 2024

      Drawing 2023-10-04 12.26.03.excalidraw

      • excalidraw
    • Dec 05, 2024

      Drawing 2023-10-04 2.excalidraw

      • excalidraw
    • Dec 05, 2024

      Drawing 2023-10-15 18.35.05.excalidraw

      • excalidraw
    • Dec 05, 2024

      Drawing 2023-10-15 18.36.19.excalidraw

      • excalidraw

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