相关论文: The eigenvalue decomposition of normal matrices by…
We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…
In this paper we present an efficient algorithm to compute the eigen decomposition of a matrix that is a weighted sum of the self outer products of vectors such as a covariance matrix of data. A well known algorithm to compute the eigen…
The numerical solution of eigenvalue problems is essential in various application areas of scientific and engineering domains. In many problem classes, the practical interest is only a small subset of eigenvalues so it is unnecessary to…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade. Here we present a new algorithm based on slicing the spectrum that takes advantage of the…
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…
We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
In this paper, we present methods for image compression on the basis of eigenvalue decomposition of normal matrices. The proposed methods are convenient and self-explanatory, requiring fewer and easier computations as compared to some…
We introduce a backward stable algorithm for computing the CS decomposition of a partitioned $2n \times n$ matrix with orthonormal columns, or a rank-deficient partial isometry. The algorithm computes two $n \times n$ polar decompositions…
The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…
We develop an accelerated algorithm for computing an approximate eigenvalue decomposition of bistochastic normalized kernel matrices. Our approach constructs a low rank approximation of the original kernel matrix by the pivoted partial…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued, pairwise orthogonal vectors. Such decompositions do not generally exist, but we show that some symmetric tensor decomposition…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…
This paper provides an accurate method to obtain the bidiagonal factorization of many generalized Pascal matrices, which in turn can be used to compute with high relative accuracy the eigenvalues, singular values and inverses of these…
We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A.