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NONLINEAR EIGENPROBLEM

Nonlinear eigenproblem

Type of equation involving matrix-valued functions

In mathematics, a nonlinear eigenproblem, sometimes nonlinear eigenvalue problem, is a generalization of the (ordinary) eigenvalue problem to equations

Nonlinear eigenproblem

Nonlinear_eigenproblem

Nonlinearity (disambiguation)

Topics referred to by the same term

mapping Nonlinear eigenproblem (AKA nonlinear eigenvalue problem), generalization of the eigenvalue problem that replaces M(λ) = A − λI Nonlinear functional

Nonlinearity (disambiguation)

Nonlinearity_(disambiguation)

Eigenvalues and eigenvectors

Concepts from linear algebra

Quantum states Jordan normal form List of numerical-analysis software Nonlinear eigenproblem Normal eigenvalue Quadratic eigenvalue problem Singular value Spectrum

Eigenvalues and eigenvectors

Eigenvalues_and_eigenvectors

SLEPc

provides solvers for different types of eigenproblems, including linear (standard and generalized) and nonlinear (quadratic, polynomial and general), as

SLEPc

Matrix pencil

Concept in linear algebra

Generalized eigenvalue problem Generalized pencil-of-function method Nonlinear eigenproblem Quadratic eigenvalue problem Generalized Rayleigh quotient Golub

Matrix pencil

Matrix_pencil

Topics referred to by the same term

software system Quadratic eigenvalue problem, a special case of nonlinear eigenproblem in mathematics QEP Resources, a defunct American energy company

QEP

Quadratic eigenvalue problem

infinite or finite, and possibly zero. This is a special case of a nonlinear eigenproblem. Q ( λ ) {\displaystyle Q(\lambda )} is also known as a quadratic

Quadratic eigenvalue problem

Quadratic_eigenvalue_problem

Delay differential equation

Type of differential equation

vertical strip of the complex plane. This characteristic equation is a nonlinear eigenproblem and there are many methods to compute the spectrum numerically.

Delay differential equation

Delay_differential_equation

Kernel method

Class of algorithms for pattern analysis

others. Most kernel algorithms are based on convex optimization or eigenproblems and are statistically well-founded. Typically, their statistical properties

Kernel method

Kernel_method

Henk van der Vorst

Dutch mathematician (born 1944)

Jacobi-Davidson method for solving ordinary, generalized, and nonlinear eigenproblems. He has analyzed convergence behavior of the conjugate gradient

Henk van der Vorst

Henk_van_der_Vorst

Algebraic Riccati equation

Nonlinear equation which arises on linear optimal control problems

An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time

Algebraic Riccati equation

Algebraic_Riccati_equation

Airy wave theory

Fluid dynamics theory on gravity waves

are related. This means that wave propagation at a fluid surface is an eigenproblem. When ω and k satisfy the dispersion relation, the wave amplitude a can

Airy wave theory

Airy_wave_theory

Divide-and-conquer eigenvalue algorithm

Algorithm on Hermitian matrices

(1981). "A Divide and Conquer Method for the Symmetric Tridiagonal Eigenproblem". Numerische Mathematik. 36 (2): 177–195. doi:10.1007/BF01396757. S2CID 120504744

Divide-and-conquer eigenvalue algorithm

Divide-and-conquer_eigenvalue_algorithm

Photonic crystal

Periodic optical nanostructure that affects the motion of photons

exploited plane wave expansion but formulates Maxwell's equation as an eigenproblem for the wave vector k while the frequency ω {\displaystyle \omega } is

Photonic crystal

Photonic_crystal

Arnoldi iteration

Iterative method for approximating eigenvectors

2007-06-30. Stewart, G. W. (2002). "A Krylov--Schur Algorithm for Large Eigenproblems". SIAM Journal on Matrix Analysis and Applications. 23 (3): 601–614

Arnoldi iteration

Arnoldi_iteration