TAUCS
swMATH ID:  4014 
Software Authors:  Sivan Toledo; Doron Chen; Vladimir Rotkin 
Description:  TAUCS: a library of sparse linear solvers. The current version of the library (1.0) includes the following functionality: Multifrontal Supernodal Cholesky Factorization. This code is quite fast (several times faster than Matlab 6’s sparse Cholesky) but not completely state of the art. It uses the BLAS to factor and compute updates from fundamental supernodes, but it does not use relaxed supernodes. LeftLooking Supernodal Cholesky Factorization. Slower than the multifrontal solver but uses less memory. DropTolerance IncompleteCholesky Factorization. Much slower than the supernodal solvers when it factors a matrix completely, but it can drop small elements from the factorization. It can also modify the diagonal elements to maintain row sums. The code uses a columnbased leftlooking approach with row lists. LDL^T Factorization. Columnbased leftlooking with row lists. Use the supernodal codes instead. OutofCore, LeftLooking Supernodal Sparse Cholesky Factorization. Solves huge systems by storing the Cholesky factors in files. Can work with factors whose size is tens of gigabytes on 32bit machines with 32bit file systems. OutofCore Sparse LU with Partial Pivoting Factor and Solve. Can solve huge unsymmetric linear systems. Ordering Codes and Interfaces to Existing Ordering Codes. The library includes a unified interface to several ordering codes, mostly existing ones. The ordering codes include Joseph Liu’s genmmd (a minimumdegree code in Fortran), Tim Davis’s amd codes (approximate minimum degree), Metis (a nesteddissection/minimumdegree code by George Karypis and Vipin Kumar), and a specialpurpose minimumdegree code for nofill ordering of treestructured matrices. All of these are symmetric orderings. Matrix Operations. Matrixvector multiplication, triangular solvers, matrix reordering. Matrix Input/Output. Routines to read and write sparse matrices using a simple file format with one line per nonzero, specifying the row, column, and value. Also routines to read matrices in HarwellBoeing format. Matrix Generators. Routines that generate finitedifferences discretizations of 2 and 3dimensional partial differential equations. Useful for testing the solvers. Iterative Solvers. Preconditioned conjugategradients and preconditioned minres. Vaidya’s Preconditioners. Augmented Maximumweightbasis preconditioners. These preconditioners work by dropping nonzeros from the coefficient matrix and them factoring the preconditioner directly. Recursive Vaidya’s Preconditioners. These preconditioners also drop nonzeros, but they don’t factor the resulting matrix completely. Instead, they eliminate rows and columns which can be eliminated without producing much fill. They then form the Schur complement of the matrix with respect to these rows and columns and drop elements from the Schur complement, and so on. During the preconditioning operation, we solve for the Schur complement elements iteratively. MultilevelSupportGraph Preconditioners. Similar to domaindecomposition preconditioners. Includes the GrembanMiller preconditioners. Utility Routines. Timers (wallclock and CPU time), physicalmemory estimator, and logging. 
Homepage:  http://www.tau.ac.il/~stoledo/taucs 
Programming Languages:  None 
Operating Systems:  None 
Dependencies:  None 
Related Software:  MUMPS; METIS; PETSc; symrcm; HSL_MA77; MA27; SparseMatrix; FITPACK; PDNET; R; FALKSOL; 3Dhp90; MKL; PARDISO; UHM; CHOLMOD; SuperLU; PointNet; CUSPARSE; CUBLAS 
Cited in:  27 Publications 
Standard Articles
2 Publications describing the Software, including 2 Publications in zbMATH  Year 

The design and implementation of a new outofcore sparse Cholesky factorization method. Zbl 1060.65580 Rotkin, Vladimir; Toledo, Sivan 
2004

Vaidya’s preconditioners: Implementation and experimental study. Zbl 1031.65064 Chen, Doron; Toledo, Sivan 
2003

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Cited by 68 Authors
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Cited in 21 Serials
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