Related papers: Incremental computation of block triangular matrix…
We present a scalable tensor-based approach to computing input-normal/output-diagonal nonlinear balancing transformations for control-affine systems with polynomial nonlinearities. This transformation is necessary to determine the states…
We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions and on interpolation, which has received little attention in…
Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive…
We consider a refinement of triangular factorization for unitary matrix valued loops.
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
In this article, we revisit some block matrix construction methods and use them to derive various general expansion formulas for calculating the ranks of matrix expressions. As applications, we derive a variety of interesting rank…
Estimation of top singular values is one of the widely used techniques and one of the intensively researched problems in Numerical Linear Algebra and Data Science. We consider here two general questions related to this problem: How top…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
We present a framework for upper bounding the number of iterations required by first-order optimization algorithms implementing constrained LQR controllers. We derive new bounds for the condition number and extremal eigenvalues of the…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
Correlation matrices are omnipresent in multivariate data analysis. When the number d of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case…
In the present paper, we propose a block variant of the extended Hessenberg process for computing approximations of matrix functions and other problems producing large-scale matrices. Applications to the computation of a matrix function…
We propose two methods to find a proper shift parameter in the shift-and-invert method for computing matrix exponential matrix-vector products. These methods are useful in the case of matrix exponential action has to be computed for a…
In this paper, we introduce the new construction of fractional derivatives and integrals with respect to a function, based on a matrix approach. We believe that this is a powerful tool in both analytical and numerical calculations. We begin…
This article derives an equation for exponentiation that can be used for calculating exponents using a parallel computing architecture.
We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…