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  2. Pseudo-spectral method - Wikipedia

    en.wikipedia.org/wiki/Pseudo-spectral_method

    They are closely related to spectral methods, but complement the basis by an additional pseudo-spectral basis, which allows representation of functions on a quadrature grid [definition needed]. This simplifies the evaluation of certain operators, and can considerably speed up the calculation when using fast algorithms such as the fast Fourier ...

  3. Spectral acceleration - Wikipedia

    en.wikipedia.org/wiki/Spectral_acceleration

    Ground motion hazard map for Hawaii, based on a 2% probability of exceeding 0.2 second spectral acceleration at 5 Hz in 50 years. Spectral acceleration (SA) is a unit measured in g (the acceleration due to Earth's gravity, equivalent to g-force) that describes the maximum acceleration in an earthquake on an object – specifically a damped, harmonic oscillator moving in one physical dimension.

  4. Pseudospectral optimal control - Wikipedia

    en.wikipedia.org/wiki/Pseudospectral_optimal_control

    There are a very large number of ideas that fall under the general banner of pseudospectral optimal control. [7] Examples of these are the Legendre pseudospectral method, the Chebyshev pseudospectral method, the Gauss pseudospectral method, the Ross-Fahroo pseudospectral method, the Bellman pseudospectral method, the flat pseudospectral method and many others.

  5. Spectral method - Wikipedia

    en.wikipedia.org/wiki/Spectral_method

    Spectral methods and finite-element methods are closely related and built on the same ideas; the main difference between them is that spectral methods use basis functions that are generally nonzero over the whole domain, while finite element methods use basis functions that are nonzero only on small subdomains (compact support).

  6. Pseudospectral knotting method - Wikipedia

    en.wikipedia.org/wiki/Pseudospectral_Knotting_Method

    In applied mathematics, the pseudospectral knotting method is a generalization and enhancement of the standard pseudospectral method for optimal control. Introduced by I. Michael Ross and F. Fahroo in 2004, it forms part of the collection of the Ross–Fahroo pseudospectral methods. [1]

  7. Pseudospectrum - Wikipedia

    en.wikipedia.org/wiki/Pseudospectrum

    In mathematics, the pseudospectrum of an operator is a set containing the spectrum of the operator and the numbers that are "almost" eigenvalues.Knowledge of the pseudospectrum can be particularly useful for understanding non-normal operators and their eigenfunctions.

  8. Split-step method - Wikipedia

    en.wikipedia.org/wiki/Split-step_method

    In numerical analysis, the split-step (Fourier) method is a pseudo-spectral numerical method used to solve nonlinear partial differential equations like the nonlinear Schrödinger equation. The name arises for two reasons.

  9. Spectral theory - Wikipedia

    en.wikipedia.org/wiki/Spectral_theory

    In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. [1] It is a result of studies of linear algebra and the solutions of systems of linear equations and their ...