Related papers: Algorithms for the computation of the matrix logar…
The Ozaki-II scheme is an emulation method that leverages the Chinese Remainder Theorem to compute high-precision matrix multiplication via a sequence of low-precision matrix multiplications. In this scheme, the attainable numerical…
We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…
SMT solvers use sophisticated techniques for polynomial (linear or non-linear) integer arithmetic. In contrast, non-polynomial integer arithmetic has mostly been neglected so far. However, in the context of program verification, polynomials…
We present an efficient algorithm to compute the induced norms of finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both induced $\mathcal{L}_2$ and terminal Euclidean norm penalties. Existing computational…
A stochastic iterative algorithm approximating second-order information using von Neumann series is discussed. We present convergence guarantees for strongly-convex and smooth functions. Our analysis is much simpler in contrast to a similar…
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…
We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how…
In this paper, we develop efficient and accurate algorithms for evaluating $\varphi(A)$ and $\varphi(A)b$, where $A$ is an $N\times N$ matrix, $b$ is an $N$ dimensional vector and $\varphi$ is the function defined by…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
In mathematical finance, a process of calibrating stochastic volatility (SV) option pricing models to real market data involves a numerical calculation of integrals that depend on several model parameters. This optimization task consists of…
We consider the setting of online logistic regression and consider the regret with respect to the 2-ball of radius B. It is known (see [Hazan et al., 2014]) that any proper algorithm which has logarithmic regret in the number of samples…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…