Influence of the Eigenvalue Spectrum on the Convergence Rate of the Conjugate Gradient Method
Alan Jennings · IMA Journal of Applied Mathematics · 1977
The analogy between the conjugate gradient method for the solution of linear simultaneous equations and a polynomial curve fitting problem provides a means of determining bounds for the convergence rate of the conjugate gradient method. Chebyshev polynomials are used to give bounds for the convergence rate associated with the main group of eigenvalues, assuming that the eigenvalues are closely spaced within the group. Additional penalty functions are developed to correct the convergence rate bounds when outlying eigenvalues are present.