15.6.4  Conjugate gradient algorithm

The conjugate_gradient command uses the conjugate gradient algorithm to solve a linear system of equations.

• conjugate_gradient takes two mandatory arguments and two optional arguments.
  • A, an n× n positive definite symmetric matrix.
  • y, a vector of length n.
  • Optionally, x₀, a vector of length n, an initial approximation.
  • ε, a positive number (by default epsilon, see Section 2.5.7, item 2.5.7).
• conjugate_gradient(A,y ⟨,x₀,ε⟩) returns the solution to Ax=y to within ε.

Examples

We can solve the system {

by entering one of the following commandlines.