Related papers: Matrix Multiplication with Less Arithmetic Complex…
Matrix-variate optimization plays a central role in advanced wireless system designs. In this paper, we aim to explore optimal solutions of matrix variables under two special structure constraints using complex matrix derivatives, including…
A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor…
he segment minimization problem consists of finding the smallest set of integer matrices that sum to a given intensity matrix, such that each summand has only one non-zero value, and the non-zeroes in each row are consecutive. This has…
The Alternating Direction Method of Multipliers (ADMM) has been studied for years. The traditional ADMM algorithm needs to compute, at each iteration, an (empirical) expected loss function on all training examples, resulting in a…
This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
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…
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…
This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…
This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…
We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…
One of the most common, but at the same time expensive operations in linear algebra, is multiplying two matrices $A$ and $B$. With the rapid development of machine learning and increases in data volume, performing fast matrix intensive…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
We present a simple randomized algorithm for approximate matrix multiplication (AMM) whose error scales with the *output* norm $\|AB\|_F$. Given any $n\times n$ matrices $A,B$ and a runtime parameter $r\leq n$, the algorithm produces in…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
With the rapid development of social network applications, social network has become an important medium for people to interact. For the minimum distance computation of all pairs in networks, Alon N[4] proposed an algorithm with matrix…
This is the second of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The first paper presented the original algorithm, its…