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Moreover, an accurate prediction has very little value without complete confidence in the level of this accuracy. It follows that we must pay careful attention, as we assemble and develop a computational model, to the accuracy of the various components of this model over the entire domain of expected validity. That a chain is no stronger than its weakest link is well known. Through a careful application of modal analysis, for example, we are often able to guarantee most of the accuracy we are achieving in a computation, in contrast to the rather pessimistic error bounds that result from an elementary error analysis. The examples provided in this seminar illustrate the development of accurate and efficient computational models appropriate for modern high performance computers, and illustrate an accuracy analysis of the sort that is required for their validation.