randUTV
swMATH ID:  30518 
Software Authors:  Martinsson, P. G.; QuintanaOrtí, G.; Heavner, N. 
Description:  randUTV: a blocked randomized algorithm for computing a rankrevealing UTV factorization. A randomized algorithm for computing a socalled UTV factorization efficiently is presented. Given a matrix A, the algorithm “randUTV” computes a factorization A = UTV*, where U and V have orthonormal columns, and T is triangular (either upper or lower, whichever is preferred). The algorithm randUTV is developed primarily to be a fast and easily parallelized alternative to algorithms for computing the Singular Value Decomposition (SVD). randUTV provides accuracy very close to that of the SVD for problems such as lowrank approximation, solving illconditioned linear systems, and determining bases for various subspaces associated with the matrix. Moreover, randUTV produces highly accurate approximations to the singular values of A. Unlike the SVD, the randomized algorithm proposed builds a UTV factorization in an incremental, singlestage, and noniterative way, making it possible to halt the factorization process once a specified tolerance has been met. Numerical experiments comparing the accuracy and speed of randUTV to the SVD are presented. Other experiments also demonstrate that in comparison to columnpivoted QR, which is another factorization that is often used as a relatively economic alternative to the SVD, randUTV compares favorably in terms of speed while providing far higher accuracy. 
Homepage:  https://dl.acm.org/citation.cfm?doid=3314951.3242670 
Source Code:  https://github.com/flame/randutv 
Keywords:  numerical linear algebra; high performance; randomized methods; rankrevealing matrix factorization; singular value decomposition 
Related Software:  rsvd; libflame; LAPACK; FLAME; RandNLA; UTV; Algorithm 1022; Algorithm 656; SuperMatrix; Algorithm 679; ScaLAPACK; TensorToolbox.jl; BSDS; tproduct; GitHub; Algorithm 971; LSRN; Blendenpik; RSVDPACK 
Cited in:  6 Documents 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

randUTV: a blocked randomized algorithm for computing a rankrevealing UTV factorization. Zbl 1471.65031 Martinsson, P. G.; QuintanaOrtí, G.; Heavner, N. 
2019

all
top 5
Cited by 10 Authors
2  Heavner, Nathan 
2  Martinsson, PerGunnar 
2  QuintanaOrtí, Gregorio 
1  Alla, Alessandro 
1  Bjarkason, Elvar K. 
1  Che, Maolin 
1  Duersch, Jed A. 
1  Igual, Francisco D. 
1  Kutz, J. Nathan 
1  Wei, Yimin 
Cited in 5 Serials
2  ACM Transactions on Mathematical Software 
1  Journal of Scientific Computing 
1  SIAM Review 
1  SIAM Journal on Scientific Computing 
1  Advances in Computational Mathematics 
Cited in 4 Fields
6  Numerical analysis (65XX) 
3  Linear and multilinear algebra; matrix theory (15XX) 
2  Computer science (68XX) 
1  Dynamical systems and ergodic theory (37XX) 