In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix , the algorithm will produce a number , which is the greatest (in absolute value) eigenvalue of , and a nonzero vector , which is a corresponding eigenvector of , that is, .
The algorithm is also known as the Von Mises iteration.[1]
Power iteration is a very simple algorithm, but it may converge slowly. The most time-consuming operation of the algorithm is the multiplication of matrix by a vector, so it is effective for a very large sparse matrix with appropriate implementation. The speed of convergence is like (see a later section). In words, convergence is exponential with base being the spectral gap.
^Richard von Mises and H. Pollaczek-Geiringer,
Praktische Verfahren der Gleichungsauflösung, ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik 9, 152-164 (1929).
In mathematics, poweriteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix A{\displaystyle A}, the algorithm...
numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method. Arnoldi finds an approximation...
the leading scores and loadings t1 and r1T by the power iteration multiplying on every iteration by X on the left and on the right, that is, calculation...
In numerical analysis, inverse iteration (also known as the inverse power method) is an iterative eigenvalue algorithm. It allows one to find an approximate...
j{\displaystyle j}th power method iterate uj{\displaystyle u_{j}} belongs to Lj,{\displaystyle {\mathcal {L}}_{j},} it follows that an iteration to produce the...
only an approximate eigenvalue, power iteration is unlikely to find it a second time. Conversely, inverse iteration based methods find the lowest eigenvalue...
solution x. Here xn is the nth approximation or iteration of x and xn+1 is the next or n + 1 iteration of x. Alternately, superscripts in parentheses are...
can be computed either iteratively or algebraically. The iterative method can be viewed as the poweriteration method or the power method. The basic mathematical...
Rayleigh quotient iteration is an eigenvalue algorithm which extends the idea of the inverse iteration by using the Rayleigh quotient to obtain increasingly...
or several times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying...
properties of poweriteration, methods relying on Krylov subspace frequently involve some orthogonalization scheme, such as Lanczos iteration for Hermitian...
is the basis of Arnoldi iteration. Alternatively, the important QR algorithm is also based on a subtle transformation of a power method. Once the eigenvalues...
available for developers to answer questions throughout the iteration. At the end of each iteration, the project stakeholders together with the customer representative...
matrix eigenvalue problem (using e.g. Jacobi eigenvalue algorithm and poweriteration) All these methods (and several others) are used to calculate physical...
preconditioning or ARPACK, MLlib for pseudo-eigenvector clustering using the poweriteration method, and R. The ideas behind spectral clustering may not be immediately...
the shift-and-invert problem by an iterative solver, e.g., the poweriteration. This gives the Inverse iteration, which normally converges to the eigenvector...
the second iteration of the toy. The third iteration, titled Beyblade Burst, was released by Takara Tomy on July 18, 2015. The fourth iteration of the toyline...
{\tfrac {4}{3}}} with each iteration. Each iteration creates four times as many line segments as in the previous iteration, with the length of each one...
situation where an iteration of the algorithm "does nothing" is called a fixed point. The strategy employed by the algorithm is iteration towards a fixed-point...
1969, the Brown Berets participated in Fred Hampton's first Black poweriteration of a Rainbow Coalition, composed of distinct and exclusive movements...
model for the Japan iteration of the area were leaked on July 8, 2019. On January 13, 2020, Universal unveiled the interactive Power-Up Bands and released...
get a power-9 transform, which has slightly more structure. Another way to create Mandelbulbs with cubic symmetry is by taking the complex iteration formula...
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