cPCG-package: Efficient and Customized Preconditioned Conjugate Gradient...

In cPCG: Efficient and Customized Preconditioned Conjugate Gradient Method for Solving System of Linear Equations

Description

Solves system of linear equations using (preconditioned) conjugate gradient algorithm, with improved efficiency using Armadillo templated 'C++' linear algebra library, and flexibility for user-specified preconditioning method. Please check <https://github.com/styvon/cPCG> for latest updates.

Details

Functions in this package serve the purpose of solving for x in Ax = b, where A is a symmetric and positive definite matrix, b is a column vector.

To improve scalability of conjugate gradient methods for larger matrices, the Armadillo templated C++ linear algebra library is used for the implementation. The package also provides flexibility to have user-specified preconditioner options to cater for different optimization needs.

The DESCRIPTION file: This package was not yet installed at build time.

Index: This package was not yet installed at build time.

Author(s)

Yongwen Zhuang

References

[1] Reeves Fletcher and Colin M Reeves. <e2><80><9c>Function minimization by conjugate gradients<e2><80><9d>. In: The computer journal 7.2 (1964), pp. 149<e2><80><93>154.

[2] David S Kershaw. <e2><80><9c>The incomplete Cholesky<e2><80><94>conjugate gradient method for the iter- ative solution of systems of linear equations<e2><80><9d>. In: Journal of computational physics 26.1 (1978), pp. 43<e2><80><93>65.

[3] Yousef Saad. Iterative methods for sparse linear systems. Vol. 82. siam, 2003.

[4] David Young. <e2><80><9c>Iterative methods for solving partial difference equations of elliptic type<e2><80><9d>. In: Transactions of the American Mathematical Society 76.1 (1954), pp. 92<e2><80><93>111.

Examples

  # generate test data
  test_A <- matrix(c(4,1,1,3), ncol = 2)
  test_b <- matrix(1:2, ncol = 1)
  
  # conjugate gradient method solver
  cgsolve(test_A, test_b, 1e-6, 1000)
  
  # preconditioned conjugate gradient method solver, 
  # with incomplete Cholesky factorization as preconditioner
  pcgsolve(test_A, test_b, "ICC")

Example output

           [,1]
[1,] 0.09090909
[2,] 0.63636364
           [,1]
[1,] 0.09074421
[2,] 0.63682348

cPCG documentation built on May 2, 2019, 11:04 a.m.