Power iteration, also known as the power method, is an eigenvalue algorithm. Given a diagonalizable matrix, it produces the eigenvalue of greatest absolute value together with a nonzero eigenvector belonging to it. The algorithm is also known as the Von Mises iteration. It is very simple, but it may converge slowly, and the speed of convergence depends on the ratio of the second largest eigenvalue to the largest one, raised to the number of iterations. The most time-consuming step is multiplying the matrix by a vector, so with a suitable implementation it is effective for very large sparse matrices.
Facts
Classification
Design Technique Connections
In Field
Source Power iteration (Wikipedia)
Uses Design Technique
Source Wolfram MathWorld: Power Method
Sources
1. Wolfram MathWorld: Power Method
Wolfram MathWorldMathWorld, article text (design technique)
is an iterative procedure for approximating a dominant eigenvalue and corresponding eigenvector of a square real matrix
Uses Design Technique: Iterative Refinement, MathWorld, article text (technique relation)
is an iterative procedure for approximating a dominant eigenvalue and corresponding eigenvector of a square real matrix
View the Source Power iteration (Wikipedia)
Lead section
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix A {\displaystyle A} , the algorithm will produce a number λ {\displaystyle \lambda } , which is the greatest (in absolute value) eigenvalue of A {\displaystyle A} , and a nonzero vector v {\displaystyle v} , which is a corresponding eigenvector of λ {\displaystyle \lambda }
In Field: Algorithms and Complexity Theory, Lead
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix A {\displaystyle A} , the algorithm will produce a number λ {\displaystyle \lambda } , which is the greatest (in absolute value) eigenvalue of A {\displaystyle A} , and a nonzero vector v {\displaystyle v} , which is a corresponding eigenvector of λ {\displaystyle \lambda } , that is, A v = λ v {\displaystyle Av=\lambda v} .
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