Related papers: Householder QR Factorization with Randomization fo…
Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…
Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called…
Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While…
Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects…
The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
The randomized block Kaczmarz (RBK) method is a widely utilized iterative scheme for solving large-scale linear systems. However, the theoretical analysis and practical effectiveness of this method heavily rely on a good row paving of the…
We present a real-time and fully integrated quantum random number generator (QRNG) by measuring laser phase fluctuations. The QRNG scheme based on laser phase fluctuations is featured for its capability of generating ultra high-speed random…
This paper addresses computational challenges in estimating Quantile Regression with Selection (QRS). The estimation of the parameters that model self-selection requires the estimation of the entire quantile process several times. Moreover,…
Solving and visualizing the potential roots of complex functions is essential in both theoretical and applied domains, yet often computationally intensive. We present a hardware-accelerated algorithm for complex function roots density graph…
We present parallel and sequential dense QR factorization algorithms for tall and skinny matrices and general rectangular matrices that both minimize communication, and are as stable as Householder QR. The sequential and parallel algorithms…
Column Generation (CG) is an effective and iterative algorithm to solve large-scale linear programs (LP). During each CG iteration, new columns are added to improve the solution of the LP. Typically, CG greedily selects one column with the…
The synthesis of a quantum circuit consists in decomposing a unitary matrix into a series of elementary operations. In this paper, we propose a circuit synthesis method based on the QR factorization via Householder transformations. We…
Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing interest in…
In recent years, machine learning methods became increasingly important for a manifold number of applications. However, they often suffer from high computational requirements impairing their efficient use in real-time systems, even when…
Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic.…
In this work, we develop randomized LU-Householder CholeskyQR (rLHC) for QR factorization of the tall-skinny matrices, consisting of SLHC3 with single-sketching and SSLHC3 with multi-sketching. Similar to LU-CholeskyQR2 (LUC2), they do not…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a…
Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…