Related papers: Adaptive multiplication of $\mathcal{H}^2$-matrice…
In this study, we propose a two-party computation protocol for approximate matrix multiplication of fixed-point numbers. The proposed protocol is provably secure under standard lattice-based cryptographic assumptions and enables matrix…
In this paper we study a worst case to average case reduction for the problem of matrix multiplication over finite fields. Suppose we have an efficient average case algorithm, that given two random matrices $A,B$ outputs a matrix that has a…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…
We investigate effects of ordering in blocked matrix--matrix multiplication. We find that submatrices do not have to be stored contiguously in memory to achieve near optimal performance. Instead it is the choice of execution order of the…
We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…
Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix…
In many applications throughout science and engineering, model reduction plays an important role replacing expensive large-scale linear dynamical systems by inexpensive reduced order models that capture key features of the original, full…
Trust-region (TR) and adaptive regularization using cubics (ARC) have proven to have some very appealing theoretical properties for non-convex optimization by concurrently computing function value, gradient, and Hessian matrix to obtain the…
Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new {\em…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…
In an iterative approach for solving linear systems with ill-conditioned, symmetric positive definite (SPD) kernel matrices, both fast matrix-vector products and fast preconditioning operations are required. Fast (linear-scaling)…
We present an adaptive grid matrix-free operator approximation scheme based on a "product-convolution" interpolation of convolution operators. This scheme is appropriate for operators that are locally translation-invariant, even if these…
This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…
Matrix trace estimation is ubiquitous in machine learning applications and has traditionally relied on Hutchinson's method, which requires $O(\log(1/\delta)/\epsilon^2)$ matrix-vector product queries to achieve a $(1 \pm…
We develop a novel linear-complexity bottom-up sketching-based algorithm for constructing a $H^2$ matrix, and present its high performance GPU implementation. The construction algorithm requires both a black-box sketching operator and an…
Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. In…
Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…