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Uzawa iteration

Index Uzawa iteration

In numerical mathematics, the Uzawa iteration is an algorithm for solving saddle point problems. [1]

10 relations: Conjugate gradient method, Gradient descent, Gram–Schmidt process, Hirofumi Uzawa, Krylov subspace, Numerical analysis, Positive-definite matrix, Saddle point, Schur complement, SIAM Journal on Numerical Analysis.

Conjugate gradient method

In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite.

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Gradient descent

Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function.

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Gram–Schmidt process

In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inner product.

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Hirofumi Uzawa

was a Japanese economist.

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Krylov subspace

In linear algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the images of b under the first r powers of A (starting from A^0.

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Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

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Positive-definite matrix

In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.

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Saddle point

In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) of orthogonal function components defining the surface become zero (a stationary point) but are not a local extremum on both axes.

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Schur complement

In linear algebra and the theory of matrices, the Schur complement of a matrix block (i.e., a submatrix within a larger matrix) is defined as follows.

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SIAM Journal on Numerical Analysis

The SIAM Journal on Numerical Analysis (SINUM; until 1965: Journal of the Society for Industrial & Applied Mathematics, Series B: Numerical Analysis) is a peer-reviewed mathematical journal published by the Society for Industrial and Applied Mathematics that covers research on the analysis of numerical methods.

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References

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

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