In mathematics, the Rayleigh quotient (/ˈreɪ.li/) for a given complex Hermitian matrix M {\displaystyle M} and nonzero vector x {\displaystyle x} is defined...

Rayleigh quotient iteration is an eigenvalue algorithm which extends the idea of the inverse iteration by using the Rayleigh quotient to obtain increasingly...

Arnoldi iteration or Lanczos iteration. Gram iteration is a super-linear and deterministic method to compute the largest eigenpair. Rayleigh quotient iteration...

(Institute of Physics) Rayleigh bandwidth (signal processing) Rayleigh quotient iteration Rayleigh's quotient in vibrations analysis Rayleigh sky model Representative...

approximation. Specifically, this is the basis for Rayleigh quotient iteration. The range of the Rayleigh quotient (for matrix that is not necessarily Hermitian)...

the Rayleigh quotient iteration, which is actually the same inverse iteration with the choice of the approximate eigenvalue as the Rayleigh quotient corresponding...

Rayleigh plot Rayleigh quotient Rayleigh quotient iteration Rayleigh's quotient in vibrations analysis Rayleigh test Rayleigh theorem Rayleigh theorem for...

iteration, μ = λ. Power iteration finds the largest eigenvalue in absolute value, so even when λ is only an approximate eigenvalue, power iteration is...

2307/1971280. JSTOR 1971280. Batterson, Steve; Smillie, John (1990). "Rayleigh quotient iteration for nonsymmetric matrices". Mathematics of Computation. 55 (191):...

vector c {\displaystyle c} is a discretized eigenvector. Rayleigh quotient Arnoldi iteration Sturm–Liouville theory Hilbert space Galerkin method Ritz...

the preconditioned Richardson iteration for solving a system of linear equations. The minimum of the Rayleigh quotient ρ ( x ) = x T A x x T x , {\displaystyle...

algorithms Arnoldi iteration Inverse iteration Jacobi method Lanczos iteration Power iteration QR algorithm Rayleigh quotient iteration Gram–Schmidt process:...

can be recognised as a Rayleigh quotient. A standard result for a positive semidefinite matrix such as XTX is that the quotient's maximum possible value...

locating the eigenvalues of a matrix Power iteration Inverse iteration Rayleigh quotient iteration Arnoldi iteration — based on Krylov subspaces Lanczos algorithm...

..8..639B. doi:10.1137/0708060. Parlett, B. N. (1974). "The Rayleigh quotient iteration and some generalizations for nonnormal matrices". Mathematics...

the Rayleigh-Ritz method on every iteration. The method performs an iterative maximization (or minimization) of the generalized Rayleigh quotient ρ (...

Hermitian matrix A {\displaystyle A} is as stationary points of the Rayleigh quotient r ( x ) = x ∗ A x x ∗ x , x ∈ C n . {\displaystyle r(x)={\frac {x^{*}Ax}{x^{*}x}}...

{\displaystyle A} , 1 / α L O N G {\displaystyle 1/\alpha ^{LONG}} is the Rayleigh quotient of A {\displaystyle A} by vector Δ x {\displaystyle \Delta x} , and...

(1970), A Three-Stage Variables-Shift Iteration for Polynomial Zeros and Its Relation to Generalized Rayleigh Iteration, Numer. Math. 14, 252–263. Ralston...

power iteration, for example, the eigenvector is actually computed before the eigenvalue (which is typically computed by the Rayleigh quotient of the...

)}} . Note that this objective is a form of the generalized Rayleigh quotient ρ ~ ( w ) = w T B w w T A w {\displaystyle {\tilde {\rho }}(w)={\frac...

improve the approximation of stress constraints. Canfield developed a Rayleigh quotient 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...