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Jacobi eigenvalue algorithm

Index Jacobi eigenvalue algorithm

In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization). [1]

17 relations: Arnold Schönhage, Carl Gustav Jacob Jacobi, Crelle's Journal, Diagonal, Eigenvalues and eigenvectors, Givens rotation, Hilbert matrix, Iterative method, Jacobi method for complex Hermitian matrices, Jacobi rotation, Mathematics of Computation, Matrix norm, Matrix similarity, Numerical linear algebra, Real number, Round-off error, Symmetric matrix.

Arnold Schönhage

Arnold Schönhage (born 1 December 1934 in Lockhausen, now Bad Salzuflen, Free State of Lippe) is a German mathematician and computer scientist.

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Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory.

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Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

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Diagonal

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

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Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

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Givens rotation

In numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes.

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Hilbert matrix

In linear algebra, a Hilbert matrix, introduced by, is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: 1 & \frac & \frac & \frac & \frac \\ \frac & \frac & \frac & \frac & \frac \\ \frac & \frac & \frac & \frac & \frac \\ \frac & \frac & \frac & \frac & \frac \\ \frac & \frac & \frac & \frac & \frac \end.

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Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

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Jacobi method for complex Hermitian matrices

In mathematics, the Jacobi method for complex Hermitian matrices is a generalization of the Jacobi iteration method.

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Jacobi rotation

In numerical linear algebra, a Jacobi rotation is a rotation, Qkℓ, of a 2-dimensional linear subspace of an n-dimensional inner product space, chosen to zero a symmetric pair of off-diagonal entries of an n×n real symmetric matrix, A, when applied as a similarity transformation: \begin \end \to \begin \end.

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Mathematics of Computation

Mathematics of Computation is a bimonthly mathematics journal focused on computational mathematics.

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Matrix norm

In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions).

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Matrix similarity

In linear algebra, two n-by-n matrices and are called similar if for some invertible n-by-n matrix.

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Numerical linear algebra

Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Round-off error

A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.

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Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

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Redirects here:

Jacobi transformation.

References

[1] https://en.wikipedia.org/wiki/Jacobi_eigenvalue_algorithm

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