Public API

Iteration(alpha, beta, x, r, p)

Record data in a single iteration within the conjugate gradient method.

cg(𝐀, 𝐛, 𝐱₀=zeros(length(𝐛)); atol=eps(), maxiter=2000)

Solves the linear system $𝐀 𝐱 = 𝐛$ using the Conjugate Gradient method.

Arguments

• 𝐀: square, symmetric, positive-definite matrix.
• 𝐛: right-hand side vector.
• 𝐱₀: initial guess for the solution. Defaults to a zero vector of appropriate length.
• atol: absolute tolerance for convergence. Defaults to machine epsilon.
• maxiter: maximum number of iterations. Defaults to 2000.

Returns

• 𝐱: the solution vector.
• iterations: an OffsetVector containing iteration history for each step.
• isconverged: a boolean indicating whether the algorithm has converged.