On Meinardus' examples for the conjugate gradient method
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On Meinardus' examples for the conjugate gradient method
The Conjugate Gradient (CG) method is widely used to solve a positive definite linear system Ax = b of order N . It is well-known that the relative residual of the kth approximate solution by CG (with the initial approximation x0 = 0) is bounded above by 2 h ∆κ + ∆ −k κ i−1 with ∆κ = √ κ + 1 √ κ− 1 , where κ ≡ κ(A) = ‖A‖2‖A−1‖2 is A’s spectral condition number. In 1963, Meinardus (Numer. Math.,...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2008
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-07-01922-9