Related papers: Ghost-OSD Method on Numerical Max-Plus Algebra
Matrix completion, where we wish to recover a low rank matrix by observing a few entries from it, is a widely studied problem in both theory and practice with wide applications. Most of the provable algorithms so far on this problem have…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
We propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves the 18th order of convergence by using only seven matrix multiplication per iteration loop. This is the record high…
In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…
Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…
This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the…
The numerical matrix Numerov algorithm is used to solve the stationary Schr\"odinger equation for central Coulomb potentials. An efficient approximation for accelerating the convergence is proposed. The Numerov method is error-prone if the…
This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…
One well adopted power grid simulation methodology is to factorize matrix once and perform only backward forward substitution with a deliberately chosen step size along the simulation. Since the required simulation time is usually long for…
We provide faster algorithms and improved sample complexities for approximating the top eigenvector of a matrix. Offline Setting: Given an $n \times d$ matrix $A$, we show how to compute an $\epsilon$ approximate top eigenvector in time…
In the past few years, successive improvements of the asymptotic complexity of square matrix multiplication have been obtained by developing novel methods to analyze the powers of the Coppersmith-Winograd tensor, a basic construction…
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…
The performance of numerical micromagnetic models is limited by the demagnetizing field computation, which typically accounts for the majority of the computation time. For magnetization dynamics simulations explicit evaluation methods are…
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…
Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Program (SDP). The main…
A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations…
One paradigm of Monte Carlo Tree Search (MCTS) improvements is to build and use state and/or action abstractions during the tree search. Non-exact abstractions, however, introduce an approximation error making convergence to the optimal…
Fast matrix multiplication is one of the most fundamental problems in algorithm research. The exponent of the optimal time complexity of matrix multiplication is usually denoted by $\omega$. This paper discusses new ideas for improving the…
We study optimization problems in a metric space $(\mathcal{X},d)$ where we can compute distances in two ways: via a ''strong'' oracle that returns exact distances $d(x,y)$, and a ''weak'' oracle that returns distances $\tilde{d}(x,y)$…
The classical division algorithm for polynomials requires $O(n^2)$ operations for inputs of size $n$. Using reversal technique and Newton iteration, it can be improved to $O({M}(n))$, where ${M}$ is a multiplication time. But the method…