相关论文: A note on the O(n)-storage implementation of the G…

Among generalized additive models, additive Mat\'ern Gaussian Processes (GPs) are one of the most popular for scalable high-dimensional problems. Thanks to their additive structure and stochastic differential equation representation,…

Karppa & Kaski (2019) proposed a novel ``broken" or ``opportunistic" matrix multiplication algorithm, based on a variant of Strassen's algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks.…

Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited…

This thesis develops signal-processing algorithms and implementation schemes under constraints of minimal parallelism and memory space, with the goal of improving energy efficiency of low-power computing hardware. We propose (i) a…

In our previous work there was some indication that Partition Sort could be having a more robust average case O(nlogn) complexity than the popular Quick Sort. In our first study in this paper, we reconfirm this through computer experiments…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

Solving linear systems of equations is a frequently encountered problem in machine learning and optimisation. Given a matrix $A$ and a vector $\mathbf b$ the task is to find the vector $\mathbf x$ such that $A \mathbf x = \mathbf b$. We…

We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in…

An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…

Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…

Graph Neural Networks (GNNs) are a powerful tool for handling structured graph data and addressing tasks such as node classification, graph classification, and clustering. However, the sparse nature of GNN computation poses new challenges…

We present a new O(k log n) algorithm of the Josephus problem. The time complexity of our algorithm is O(k log n), and this time complexity is on a par with the existing O(k log n) algorithm. We do not have any recursion overhead or stack…

We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a…

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…

The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…

Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications. Quantum computing, with its inherent parallelism and exponential storage…

In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…

Recent work by Elmasry et al. (STACS 2015) and Asano et al. (ISAAC 2014), reconsidered classical fundamental graph algorithms focusing on improving the space complexity. We continue this line of work focusing on space. Our first result is a…

This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…

A modified dynamic programming algorithm rapidly and accurately solves large 0/1 knapsack problems. It has computational O(nlogn), space O(nlogn) and predictable maximum error. Experimentally it's accuracy increases faster than linearly…