相关论文: Real dqds for the nonsymmetric tridiagonal eigenva…
In this short note, we present a novel method for computing exact lower and upper bounds of eigenvalues of a symmetric tridiagonal interval matrix. Compared to the known methods, our approach is fast, simple to present and to implement, and…
This work presents a novel approach to compute the eigenvalues of non-Hermitian matrices using an enhanced shifted QR algorithm. The existing QR algorithms fail to converge early in the case of non-hermitian matrices, and our approach shows…
We consider the numerical solution of large-scale M-matrix algebraic Riccati equations with low-rank structures. We derive a new doubling iteration, decoupling the four original iteration formulae in the alternating-directional doubling…
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
Inverse iteration is known to be an effective method for computing eigenvectors corresponding to simple and well-separated eigenvalues. In the non-symmetric case, the solution of shifted Hessenberg systems is a central step. Existing…
It is known that every real orthogonal matrix can be brought into the domain of the Cayley transform by multiplication with a suitable diagonal signature matrix. In this paper we provide a constructive and numerically efficient algorithm…
This paper analyzes a special instance of nonsymmetric algebraic matrix Riccati equations arising from transport theory. Traditional approaches for finding the minimal nonnegative solution of the matrix Riccati equations are based on the…
This paper proposes a harmonic Lanczos bidiagonalization method for computing some interior singular triplets of large matrices. It is shown that the approximate singular triplets are convergent if a certain Rayleigh quotient matrix is…
We present a novel algorithm for calculating the discrete fractional Hadamard transform for data vectors whose size N is a power of two. A direct method for calculation of the discrete fractional Hadamard transform requires $N^2$…
In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…
We introduce a novel eigenvalue algorithm for near-diagonal matrices inspired by Rayleigh-Schr\"odinger perturbation theory and termed Iterative Perturbative Theory (IPT). Contrary to standard eigenvalue algorithms, which are either…
The Schur decomposition of a square matrix $A$ is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…
We develop two fast algorithms for Hessenberg reduction of a structured matrix $A = D + UV^H$ where $D$ is a real or unitary $n \times n$ diagonal matrix and $U, V \in\mathbb{C}^{n \times k}$. The proposed algorithm for the real case…
The principal minors of a tridiagonal matrix satisfy two-term and three-term recurrences [1, 2]. Based on these facts, the current article presents a new efficient and reliable hybrid numerical algorithm for evaluating general n-th order…
We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers. In doing so, we unify some matrix decompositions: For…
The eigenvalue shift technique is the most well-known and fundamental tool for matrix computations. Applications include the search of eigeninformation, the acceleration of numerical algorithms, the study of Google's PageRank. The shift…
The power method is a basic method for computing the dominant eigenpair of a matrix. In this paper, we propose a structure-preserving power-like method for computing the dominant conjugate pair of purely imaginary eigenvalues and the…
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…