Results 291 to 300 of about 910,007 (330)

Minimizing the Profile of a Symmetric Matrix

SIAM Journal on Scientific Computing, 2002
Two classes of methods for optimizing the profile of a sparse matrix are given. Profile storage is useful when the matrix is moderately sparse, or when the nonzero entries are near the main diagonal. The proposed methods in the first class are heuristic.
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Symmetric Matrix Eigenvalue Techniques

2006
The article describes symmetric matrix eigenvalue techniques: basic methods (power method, inverse iteration, orthogonal iteration and QR iteration), tridiagonalization and implicitly shifted QR method, divide-and-conquer method, bisection and inverse iteration, the method of multiple relatively robust representations, Jacobi method and Lanczos method.
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Reducing the Symmetric Matrix Eigenvalue Problem to Matrix Multiplications

SIAM Journal on Scientific Computing, 1993
One important issue for matrix eigenvalue problems on high performance parallel computers is the cost of data movement. The paper shows that the eigenvalues and eigenvectors of a symmetric \(n\times n\) matrix can be found by \(O(\log_ 2n)\) matrix multiplications.
Yau, Shing-Tung, Lu, Ya Yan
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On the Sum of the Largest Eigenvalues of a Symmetric Matrix

SIAM Journal on Matrix Analysis and Applications, 1992
The sum of the largest \(k\) eigenvalues of a symmetric matrix has an extremal property that was given by \textit{Ky Fan} [Proc. Natl. Acad. Sci. USA 35, 652--655 (1949; Zbl 0041.00602)]. A simple proof of this property is discussed in this paper. The key step of this proof is based on the observation that the convex hull of the set of projection ...
Overton, Michael L., Womersley, Robert S.   +1 more
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An algorithm for matrix symmetrization

Journal of the Franklin Institute, 1981
Abstract In this paper we characterize a symmetrizability property using the theory of output sets. Employing the basic properties of symmetric matrices and an efficient algorithm for systematic generation of output sets, an algorithm for testing the symmetrizability of a matrix is presented and illustrated.
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Tridiagonalization of a symetric band matrix

Numerische Mathematik, 1968
The well known method proposed by Givens [1] reduces a full symmetric matrix A = (a ik ) of order n by a sequence of appropriately chosen elementary orthogonal transformations (in the following called Jacobi rotations) to triput diagonal form. This is achieved by (n - 1)(n - 2)/2 Jacobi rotations, each of which annihilates one of the elements a ik with
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Calculation of a Constrained Minimal Symmetric Matrix

SIAM Journal on Applied Mathematics, 1974
A procedure is derived for calculating a symmetric matrix, P, with minimal sum of the squares of its elements, which satisfies $PB = A$. B and A are rectangular or square matrices. It is necessary that $AB^ + B = A$, which is not a trivial requirement if B has more columns than rows, or if B is not of full rank.
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The biofilm matrix: multitasking in a shared space

Nature Reviews Microbiology, 2022
Hans-Curt Flemming, Eric D Van Hullebusch, Thomas R Neu   +2 more
exaly  

Extracellular vesicle–matrix interactions

Nature Reviews Materials, 2023
, Jae-won Shin
exaly  

Symmetric matrix

2001
Saul I. Gass, Carl M. Harris
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