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Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…
Value Iteration is a widely used algorithm for solving Markov Decision Processes (MDPs). While previous studies have extensively analyzed its convergence properties, they primarily focus on convergence with respect to the infinity norm. In…
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely…
Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate…
We investigate the power iteration algorithm for the tensor PCA model introduced in Richard and Montanari (2014). Previous work studying the properties of tensor power iteration is either limited to a constant number of iterations, or…
In this paper, we propose a cone projected power iteration algorithm to recover the first principal eigenvector from a noisy positive semidefinite matrix. When the true principal eigenvector is assumed to belong to a convex cone, the…
In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential…
In this paper, we first study the projections onto the set of unit dual quaternions, and the set of dual quaternion vectors with unit norms. Then we propose a power method for computing the dominant eigenvalue of a dual quaternion Hermitian…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
We study the general approach to accelerating the convergence of the most widely used solution method of Markov decision processes with the total expected discounted reward. Inspired by the monotone behavior of the contraction mappings in…
The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The…
This paper investigates the eigenvalue computation problem of the dual quaternion Hermitian matrix closely related to multi-agent group control. Recently, power method was proposed by Cui and Qi in Journal of Scientific Computing, 100…
Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…
Iterative methods for computing matrix functions have been extensively studied and their convergence speed can be significantly improved with the right tuning of parameters and by mixing different iteration types. Handtuning the design…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
In recent years, the PageRank algorithm has garnered significant attention due to its crucial role in search engine technologies and its applications across various scientific fields. It is well-known that the power method is a classical…
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…