Summary
This paper describes upper and lowerp-norm error bounds for approximate solutions of the linear system of equationsAx=b. These bounds imply that the error is proportional to the quantity\(\left\| r \right\|_2^2 \left\| {A^T r} \right\|_q^{ - 1} \) wherer is the residual andq is the conjugate index top. The constant of proportionality is larger than 1 and lies in a specified range. Similar results are obtained for approximations toA −1 and solutions of nonsingular linear equations on general spaces.
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References
Golub, G.H., van Loan, C.F. (1983): Matrix Computations. Johns Hopkins University Press, Baltimore
Householder, A.S. (1975): The Theory of Matrices in Numerical Analysis. Dover Publications, New York
Luenberger, D.G. (1984): Linear and Nonlinear Programming, 2nd ed. Addison-Wesley, Reading
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Research was partially supported by NSF Grant DMS8901477