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  2. Matrix regularization - Wikipedia

    en.wikipedia.org/wiki/Matrix_regularization

    There are a number of matrix norms that act on the singular values of the matrix. Frequently used examples include the Schatten p-norms, with p = 1 or 2. For example, matrix regularization with a Schatten 1-norm, also called the nuclear norm, can be used to enforce sparsity in the spectrum of a matrix.

  3. Hurwitz matrix - Wikipedia

    en.wikipedia.org/wiki/Hurwitz_matrix

    The Routh–Hurwitz matrix associated to a polynomial is a particular matrix whose non-zero entries are all coefficients of the polynomial. Topics referred to by the same term This disambiguation page lists articles associated with the title Hurwitz matrix .

  4. Routh–Hurwitz stability criterion - Wikipedia

    en.wikipedia.org/wiki/Routh–Hurwitz_stability...

    In the control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system. A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as ...

  5. Stable polynomial - Wikipedia

    en.wikipedia.org/wiki/Stable_polynomial

    A linear system is BIBO stable if its characteristic polynomial is stable. The denominator is required to be Hurwitz stable if the system is in continuous-time and Schur stable if it is in discrete-time. In practice, stability is determined by applying any one of several stability criteria.

  6. Stability theory - Wikipedia

    en.wikipedia.org/wiki/Stability_theory

    One of the key ideas in stability theory is that the qualitative behavior of an orbit under perturbations can be analyzed using the linearization of the system near the orbit. In particular, at each equilibrium of a smooth dynamical system with an n -dimensional phase space , there is a certain n × n matrix A whose eigenvalues characterize the ...

  7. Numerical stability - Wikipedia

    en.wikipedia.org/wiki/Numerical_stability

    Von Neumann stability analysis is a commonly used procedure for the stability analysis of finite difference schemes as applied to linear partial differential equations. These results do not hold for nonlinear PDEs, where a general, consistent definition of stability is complicated by many properties absent in linear equations.

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