Numerical stability of the Chebyshev method for the solution of large linear systems
نویسندگان
چکیده
This paper contains the rounding error analysis for the Chebyshev method for the solution of large linear systems Ax+g = 0 where A = A is positive definite. We prove that the Chebyshev method in floating point arithmetic is numerically stable, which means that the computed sequence {x^} approximates the solution a such that lim|k is of order C||a||.||A~ \\.\\y\\ where £ is the relative computer precision, k We also point out that in general the Chebyshev method is not well-behaved, which means that x^, k large, is not the exact solution for a slightly perturbed A or equivalently that the computed residuals r k = Axk+g are of order C||a|| II*" || ||or||.
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