24 episodes

Nick Trefethen FRS, Professor of Numerical Analysis at Oxford University, teaches a course for DPhil (PhD) students across all the science departments at the university. The course is distinctive for its exceptionally strong conceptual basis, focussing on fundamental ideas of numerical algorithms and the world of science and engineering they sustain. Historical and philosophical notes on many subjects make these lectures unusual, offering deeper understanding and new perspectives for anyone involved with numerical analysis or scientific computing.

Scientific Computing for DPhil Students Oxford University

    • Education
    • 5.0 • 3 Ratings

Nick Trefethen FRS, Professor of Numerical Analysis at Oxford University, teaches a course for DPhil (PhD) students across all the science departments at the university. The course is distinctive for its exceptionally strong conceptual basis, focussing on fundamental ideas of numerical algorithms and the world of science and engineering they sustain. Historical and philosophical notes on many subjects make these lectures unusual, offering deeper understanding and new perspectives for anyone involved with numerical analysis or scientific computing.

    • video
    Sparse Matrices and Iterative Methods (1.1)

    Sparse Matrices and Iterative Methods (1.1)

    In this lecture, Professor Trefethen first provides an overview of the field of linear algebra and optimization. Secondly, he discusses the question of how fast we can solve Ax=3Db? Thirdly, he discusses sparse matrices Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

    • 50 min
    • video
    Sparse Matrices and Iterative Methods (1.2)

    Sparse Matrices and Iterative Methods (1.2)

    In this lecture, Professor Trefethen discusses the topic of conjugate gradients and the convergence of CG. Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

    • 53 min
    • video
    Sparse Matrices and Iterative Methods (1.3)

    Sparse Matrices and Iterative Methods (1.3)

    In this lecture, Professor Trefethen discusses preconditioned CG and also provides examples of preconditioners Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

    • 54 min
    • video
    Sparse Matrices and Iterative Methods (1.4)

    Sparse Matrices and Iterative Methods (1.4)

    In this lecture, Professor Trefethon provides a definition of numerical analysis and provides an overview of matrix iterations, including a discussion on the Lanczos iteration. He also reviews various numerical software tools and information sources. Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

    • 48 min
    • video
    Dense Linear Algebra (2.1)

    Dense Linear Algebra (2.1)

    In this lecture, Professor Trefethen discusses matrices, vectors and expansions, including orthogonal vectors and matrices. Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

    • 52 min
    • video
    Dense Linear Algebra (2.2)

    Dense Linear Algebra (2.2)

    In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear least-squares. Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

    • 49 min

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