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Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…
Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to…
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…
In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by…
We present a dynamic algorithm for maintaining $(1+\epsilon)$-approximate maximum eigenvector and eigenvalue of a positive semi-definite matrix $A$ undergoing \emph{decreasing} updates, i.e., updates which may only decrease eigenvalues.…
Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion…
The problem of connectivity assessment in an asymmetric network represented by a weighted directed graph is investigated in this article. A power iteration algorithm in a centralized implementation is developed first to compute the…
Despite advancements in deep reinforcement learning algorithms, developing an effective exploration strategy is still an open problem. Most existing exploration strategies either are based on simple heuristics, or require the model of the…
We study the problem of computing the largest root of a real rooted polynomial $p(x)$ to within error $\varepsilon $ given only black box access to it, i.e., for any $x \in {\mathbb R}$, the algorithm can query an oracle for the value of…
The recursive Neville algorithm allows one to calculate interpolating functions recursively. Upon a judicious choice of the abscissas used for the interpolation (and extrapolation), this algorithm leads to a method for convergence…
A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…
We address the general mathematical problem of computing the inverse $p$-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary $p$-th roots and their inverses of…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
Matrix diagonalization is at the cornerstone of numerous fields of scientific computing. Diagonalizing a matrix to solve an eigenvalue problem requires a sequential path of iterations that eventually reaches a sufficiently converged and…
We consider the eigenvalue problem $Ax = \lambda x$ where $A \in \mathbb{R}^{n \times n}$ and the eigenvalue is also real $\lambda \in \mathbb{R}$. If we are given $A$, $\lambda$ and, additionally, the absolute value of the entries of $x$…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
The power method is a classical algorithm with broad applications in machine learning tasks, including streaming PCA, spectral clustering, and low-rank matrix approximation. The distilled purpose of the vanilla power method is to determine…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…