The algorithms of inverse iteration and Rayleigh quotient iteration for approximating an eigenpair of a matrix contain a step in which a matrix-vector equation must be solved.The behaviour of these algorithms is analysed if this equation is solved only approximately with a known tolerance.

When a designed experiment is conducted, the exact levels of controlled experimental variables specified by the design may not be attainable. Two different types of situations can occur in which the actual settings of the design variables deviate from the target design settings. In one case, the...