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This paper contains the rounding error analysis for the Chebyshev method for the solution of large linear systemsAx+g=0 whereA=A * is positive definite. We prove that the Chebyshev method in floating point arithmetic is numerically stable, which means that the computed sequence {x k} approximates the solution ¿ such that $$\\overline {\\mathop {\\lim }\\limits_k } $$ ¿x k ¿¿¿ is of order ¿¿A¿¿A ¿1¿¿¿¿ where ¿ is the relative computer precision.We also point out that in general the Chebyshev method is not well-behaved, which means that the computed residualsr k=Ax k+g are of order ¿¿A¿2¿A ¿1¿¿¿¿.

Numerical stability of the Chebyshev method for the solution of large linear systems