Bounds for the error of linear systems of equations using the theory of moments |
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| Authors: | Germund Dahlquist |
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| Institution: | Royal Institute of Technology, Stockholm 70, Sweden; Department of Computer Science, Stanford University, Stanford, California 94305 USA |
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| Abstract: | Consider the system, of linear equations Ax = b where A is an n × n real symmetric, positive definite matrix and b is a known vector. Suppose we are given an approximation to x, ξ, and we wish to determine upper and lower bounds for ∥ x − ξ ∥ where ∥ ··· ∥ indicates the euclidean norm. Given the sequence of vectors {ri}ik = 0, where ri = Ari − 1 and r0 = b − Aξ, it is shown how to construct a sequence of upper and lower bounds for ∥ x − ξ ∥ using the theory of moments. |
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