Rayleigh quotient iteration is an eigenvalue algorithm which extends the idea of the inverse iteration by using the Rayleigh quotient to obtain increasingly accurate eigenvalue estimates.
Rayleigh quotient iteration is an iterative method, that is, it delivers a sequence of approximate solutions that converges to a true solution in the limit. Very rapid convergence is guaranteed and no more than a few iterations are needed in practice to obtain a reasonable approximation. The Rayleigh quotient iteration algorithm converges cubically for Hermitian or symmetric matrices, given an initial vector that is sufficiently close to an eigenvector of the matrix that is being analyzed.
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Rayleighquotientiteration is an eigenvalue algorithm which extends the idea of the inverse iteration by using the Rayleighquotient to obtain increasingly...
In mathematics, the Rayleighquotient (/ˈreɪ.li/) for a given complex Hermitian matrix M {\displaystyle M} and nonzero vector x {\displaystyle x} is defined...
Arnoldi iteration or Lanczos iteration. Gram iteration is a super-linear and deterministic method to compute the largest eigenpair. Rayleighquotient iteration...
the Rayleighquotientiteration, which is actually the same inverse iteration with the choice of the approximate eigenvalue as the Rayleighquotient corresponding...
approximation. Specifically, this is the basis for Rayleighquotientiteration. The range of the Rayleighquotient (for matrix that is not necessarily Hermitian)...
iteration, μ = λ. Power iteration finds the largest eigenvalue in absolute value, so even when λ is only an approximate eigenvalue, power iteration is...
eigenvalue closest to the shift α{\displaystyle \alpha }. The Rayleighquotientiteration is a shift-and-invert method with a variable shift. Spectral...
Hermitian matrix A{\displaystyle A} is as stationary points of the Rayleighquotient r(x)=x∗Axx∗x,x∈Cn.{\displaystyle r(x)={\frac {x^{*}Ax}{x^{*}x}},\qquad...
the Rayleigh-Ritz method on every iteration. The method performs an iterative maximization (or minimization) of the generalized Rayleighquotient ρ(x):=ρ(A...
locating the eigenvalues of a matrix Power iteration Inverse iterationRayleighquotientiteration Arnoldi iteration — based on Krylov subspaces Lanczos algorithm...
can be recognised as a Rayleighquotient. A standard result for a positive semidefinite matrix such as XTX is that the quotient's maximum possible value...
^{2}={\frac {B[Y(x)]}{A[Y(x)]}}=R[Y(x)]} which is also known as the Rayleighquotient. Thus, if we knew the mode shape Y(x){\displaystyle Y(x)}, we would...
power iteration, for example, the eigenvector is actually computed before the eigenvalue (which is typically computed by the Rayleighquotient of the...
)}}. Note that this objective is a form of the generalized Rayleighquotient ρ~(w)=wTBwwTAw{\displaystyle {\tilde {\rho }}(w)={\frac {w^{T}Bw}{w^{T}Aw}}}...
improve the approximation of stress constraints. Canfield developed a Rayleighquotient approximation to improve the accuracy of eigenvalue approximations...
measure surface tension, published several papers and was credited by Lord Rayleigh and Irving Langmuir. Mass spectrometry Sybil M. Rock developed the mathematical...
{\displaystyle f=(I-T)^{-1}h=h+Th+T^{2}h+T^{3}h+\cdots } This iterative scheme is often called Picard iteration after the French mathematician Charles Émile Picard...
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