randomized numerical linear algebrarandomized SVDrank‐revealing methodsMany model order reduction (MOR) methods employ a reduced basis V ∈ IRm × k to approximate the state variables. For nonlinear models, V is often computed using the snapshot method. The associated low‐rank approximation of ...
More significantly, we achieve these improvements by arguing that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise; these are powerful and standard techniques in randomized numerical linear algebra. With this recognition, we are...
while linear algebra algorithms have been of interest for decades in areas such as numerical linear algebra (NLA) and scientific computing, in recent years, there has been renewed interest in developing matrix algorithms that are appropri...
The power method and block Lanczos method are popular numerical algorithms for computing the truncated singular value decomposition (SVD) and eigenvalue decomposition problems. Especially in the literature of randomized numerical linear algebra, the power method is widely applied to improve the quality ...
Recent years have witnessed an explosion of research on so-called Randomized Numerical Linear Algebra [4] (or RandNLA for short) algorithms, which leverage the power of randomization in order to perform standard matrix computations. One of the core problems that have been extensively researched in...
Numerical Linear Algebra (SIAM, 1997). Saad, Y. Iterative Methods for Sparse Linear Systems (SIAM, 2003). Strohmer, T. & Vershynin, R. A randomized Kaczmarz algorithm with exponential convergence. J. Fourier Anal. Appl. 15, 262 (2007). Article MathSciNet Google Scholar Harrow, A. W...
Randomized Pivoting and Spectrum-Revealing Bounds in Numerical Linear Algebra 来自 掌桥科研 喜欢 0 阅读量: 46 作者: CB Melgaard 摘要: In the first part of this dissertation, we explore a novel randomized pivoting strategy to efficiently improve the reliability and quality of the LU factorization...
Gittens AA (2013) Topics in randomized numerical linear algebra. California Institute of Technology, Pasadena MATH Google Scholar Halko N, Martinsson P-G, Tropp JA (2011) Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev 53(2):217...
Given input–output pairs of an elliptic partial differential equation (PDE) in three dimensions, we derive the first theoretically rigorous scheme fo
The partially randomized extended Kaczmarz method with residual is effective for solving large sparse linear systems. In this paper, an improved variant of this method is proposed and its expected exponential convergence rate is proved. In addition, numerical results show that this method can preform...