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Search.setIndex({"alltitles": {"Access to computers": [[12, "access-to-computers"]], "Accreditation": [[11, "accreditation"]], "Adjoints and Hermitian matrices": [[1, "adjoints-and-hermitian-matrices"]], "An algorithm for LU decomposition": [[4, "an-algorithm-for-lu-decomposition"]], "An example matrix (Non-examinable in 2024/25)": [[7, "an-example-matrix-non-examinable-in-2024-25"]], "Analysing algorithms": [[3, null]], "Application: Least squares problems": [[2, "application-least-squares-problems"]], "Arnoldi iteration": [[6, "arnoldi-iteration"]], "Assessment": [[11, "assessment"]], "Assumed knowledge": [[11, "assumed-knowledge"]], "Backward stability for solving a linear system using QR": [[3, "backward-stability-for-solving-a-linear-system-using-qr"]], "Backward stability of the Householder algorithm": [[3, "backward-stability-of-the-householder-algorithm"]], "Blackboard": [[11, "blackboard"]], "Chebyshev acceleration (examinable in 2024/25)": [[7, "chebyshev-acceleration-examinable-in-2024-25"]], "Cholesky factorisation": [[4, "cholesky-factorisation"]], "Coding style and commenting": [[0, "coding-style-and-commenting"]], "Computational tools": [[12, null]], "Condition number": [[3, "condition-number"]], "Conditioning of linear algebra computations": [[3, "conditioning-of-linear-algebra-computations"]], "Connections between power iteration, inverse iteration, and QR algorithm": [[5, "connections-between-power-iteration-inverse-iteration-and-qr-algorithm"]], "Constructing orthogonal projectors from sets of orthonormal vectors": [[1, "constructing-orthogonal-projectors-from-sets-of-orthonormal-vectors"]], "Convergence analysis for Richardson": [[7, "convergence-analysis-for-richardson"]], "Convergence analysis for symmetric matrices": [[7, "convergence-analysis-for-symmetric-matrices"]], "Convergence criteria for stationary methods": [[7, "convergence-criteria-for-stationary-methods"]], "Convergence of GMRES": [[6, "convergence-of-gmres"]], "Course leader": [[11, "course-leader"]], "Editing code": [[12, "editing-code"]], "Errata for 2024/25": [[9, null]], "Finding eigenvalues of matrices": [[5, null]], "Floating point numbers and arithmetic": [[3, "floating-point-numbers-and-arithmetic"]], "GMRES": [[6, "gmres"]], "General course information": [[11, null]], "Getting ready for computational exercises": [[0, null]], "Getting started with git and GitHub": [[12, "getting-started-with-git-and-github"]], "Getting the software that you need": [[0, "getting-the-software-that-you-need"]], "GitHub and git": [[0, "github-and-git"], [12, "github-and-git"]], "Householder triangulation": [[2, "householder-triangulation"]], "How to do the computational exercises": [[0, "how-to-do-the-computational-exercises"]], "How to find eigenvalues?": [[5, "how-to-find-eigenvalues"]], "Inner products and orthogonality": [[1, "inner-products-and-orthogonality"]], "Installing the course package to the venv": [[0, "installing-the-course-package-to-the-venv"]], "Inverse iteration": [[5, "inverse-iteration"]], "Invertibility and inverses": [[1, "invertibility-and-inverses"]], "Iterative Krylov methods for Ax=b": [[6, null]], "Knowing when to stop": [[6, "knowing-when-to-stop"]], "Krylov subspace methods": [[6, "krylov-subspace-methods"]], "LU decomposition": [[4, null]], "Lecture notes:": [[10, null]], "Linear algebra preliminaries": [[1, null]], "Mastery": [[11, "mastery"]], "Matrices, vectors and matrix-vector multiplication": [[1, "matrices-vectors-and-matrix-vector-multiplication"]], "Matrix norms for discussing stability": [[3, "matrix-norms-for-discussing-stability"]], "Modified Gram-Schmidt": [[2, "modified-gram-schmidt"]], "Modified Gram-Schmidt as triangular orthogonalisation": [[2, "modified-gram-schmidt-as-triangular-orthogonalisation"]], "Module contents": [[8, "module-cla_utils"]], "Norm inequalities": [[3, "norm-inequalities"]], "Operation count": [[3, "operation-count"]], "Operation count for Householder": [[3, "operation-count-for-householder"]], "Operation count for modified Gram-Schmidt": [[3, "operation-count-for-modified-gram-schmidt"]], "Orthogonal components of a vector": [[1, "orthogonal-components-of-a-vector"]], "Pivoting": [[4, "pivoting"]], "Power iteration": [[5, "power-iteration"]], "Preconditioned GMRES": [[6, "preconditioned-gmres"]], "Preconditioning Krylov methods": [[7, null]], "Projector interpretation of Gram-Schmidt": [[2, "projector-interpretation-of-gram-schmidt"]], "Projectors and projections": [[1, "projectors-and-projections"]], "Python": [[12, "python"]], "Python virtual environment": [[0, "python-virtual-environment"]], "QR factorisation": [[2, null]], "QR factorisation by classical Gram-Schmidt algorithm": [[2, "qr-factorisation-by-classical-gram-schmidt-algorithm"]], "Raising hell issues": [[12, "raising-hell-issues"]], "Range, nullspace and rank": [[1, "range-nullspace-and-rank"]], "Rayleigh quotient": [[5, "rayleigh-quotient"]], "Rayleigh quotient iteration": [[5, "rayleigh-quotient-iteration"]], "Running your work": [[0, "running-your-work"]], "Setting up your repository": [[0, "setting-up-your-repository"]], "Sharing your problems with gists": [[12, "sharing-your-problems-with-gists"]], "Similarity transformation to upper Hessenberg form": [[5, "similarity-transformation-to-upper-hessenberg-form"]], "Simultaneous iteration": [[5, "simultaneous-iteration"]], "Skeleton code documentation": [[0, "skeleton-code-documentation"]], "Splitting methods as preconditioners": [[7, "splitting-methods-as-preconditioners"]], "Stability": [[3, "stability"]], "Stability of LU factorisation": [[4, "stability-of-lu-factorisation"]], "Stationary iterative methods": [[7, "stationary-iterative-methods"]], "Submodules": [[8, "submodules"]], "Symmetric iterative methods": [[7, "symmetric-iterative-methods"]], "Taking advantage of matrix structure": [[4, "taking-advantage-of-matrix-structure"]], "Testing your work": [[0, "testing-your-work"]], "The Terminal": [[0, "the-terminal"]], "The command line": [[12, "the-command-line"]], "The practical QR algorithm": [[5, "the-practical-qr-algorithm"]], "The pure QR algorithm": [[5, "the-pure-qr-algorithm"]], "The pure QR algorithm and simultaneous iteration are equivalent": [[5, "the-pure-qr-algorithm-and-simultaneous-iteration-are-equivalent"]], "Transformations to Schur factorisation": [[5, "transformations-to-schur-factorisation"]], "Unitary matrices": [[1, "unitary-matrices"]], "Using splitting methods as preconditioners": [[7, "using-splitting-methods-as-preconditioners"]], "Using the Windows machines in the computer labs": [[12, "using-the-windows-machines-in-the-computer-labs"]], "Using your own machine": [[12, "using-your-own-machine"]], "Vector norms": [[1, "vector-norms"]], "What is the QR factorisation?": [[2, "what-is-the-qr-factorisation"]], "Your first programming exercises": [[1, "your-first-programming-exercises"]], "cla_utils package": [[8, 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