相关论文: An Efficient Algorithm for Latin Squares in a Bipa…
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigenvectors. In this article we propose a new method for…
This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
In this paper we compare the candidates to be spectral minimal partitions for two criteria: the maximum and the average of the first eigenvalue on each subdomains of the partition. We analyze in detail the square, the disk and the…
A deflated and restarted Lanczos algorithm to solve hermitian linear systems, and at the same time compute eigenvalues and eigenvectors for application to multiple right-hand sides, is described. For the first right-hand side, eigenvectors…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…
This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
Latin squares and hypercubes are combinatorial designs with several applications in statistics, cryptography and coding theory. In this paper, we generalize a construction of Latin squares based on bipermutive cellular automata (CA) to the…
Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…
For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues. The algorithm is based on the…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
We propose NEP_MiniMax, a novel computational method for solving nonlinear eigenvalue problems (NEPs) $T(\lambda)\mathbf{u}= 0$ on compact continua $\Omega \subset \mathbb{C}$. The method combines two key components: (1) a rational minimax…
In this note, we present an algorithm that yields many new methods for constructing doubly stochastic and symmetric doubly stochastic matrices for the inverse eigenvalue problem. In addition, we introduce new open problems in this area that…
A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…