相关论文: Analysis of Randomized Householder-Cholesky QR Fac…

We introduce an algorithmic framework for performing QR factorization with column pivoting (QRCP) on general matrices. The framework enables the design of practical QRCP algorithms through user-controlled choices for the core subroutines.…

We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov…

Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard…

As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…

The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…

Randomly pivoted Cholesky (RPCholesky) is an algorithm for constructing a low-rank approximation of a positive-semidefinite matrix using a small number of columns. This paper develops an accelerated version of RPCholesky that employs block…

Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…

We classify a family of matrices of shift operators that can be factorised in a computationally tractable manner with the Cholesky algorithm. Such matrices arise in the linear quadratic regulator problem, and related areas. We use the…

We discuss a randomized strong rank-revealing QR factorization that effectively reveals the spectrum of a matrix $\textbf{M}$. This factorization can be used to address problems such as selecting a subset of the columns of $\textbf{M}$,…

Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case).…

In this work, by employing a bitsliced data representation as building blocks of algorithms, we showcase the capability and scalability of our proposed method in a variety of PRNG methods in the category of block and stream ciphers. While…

Randomized compiling (RC) is an efficient method for tailoring arbitrary Markovian errors into stochastic Pauli channels. However, the standard procedure for implementing the protocol in software comes with a large experimental overhead --…

Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…

Estimating large covariance matrices has been a longstanding important problem in many applications and has attracted increased attention over several decades. This paper deals with two methods based on pre-existing works to impose sparsity…

This paper introduces sTiles, a GPU-accelerated framework for factorizing sparse structured symmetric matrices. By leveraging tile algorithms for fine-grained computations, sTiles uses a structure-aware task execution flow to handle…

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…

We present Flip-Flop Spectrum-Revealing QR (Flip-Flop SRQR) factorization, a significantly faster and more reliable variant of the QLP factorization of Stewart, for low-rank matrix approximations. Flip-Flop SRQR uses SRQR factorization to…

Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is…

We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product…

This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…