Abstract.Suppose that a method q~ computes an approximation of the exact solution of a linear system Ax=b with the relative error q, q < 1. We prove that if all computations are performed in floating point arithmetic fl and single precision, then q~ with iterative refinement is numerically stable and well-behaved whenever qHAll ItA-1LL is at most of order unity.
Because they are easy to administer, rating scales are often used as proxies for utility measures. The authors investigated the relationship between time-tradeoff utilities and rating scale values in two populations: 124 cancer patients asked to evaluate their current states of health and 102 relatives and close friends of cancer patients asked to evaluate health-state scenarios. None of the models tested effectively described the relationship between individual patients' rating scale values and time-tradeoff utilities for their current states of health. In contrast, both a plateau and a power-function model explained the variability in the responses of the relatives reasonably well (R2 = 0.56 and R2 = 0.58, respectively). Given that many respondents who were unwilling to trade off any time assigned rating scale values of well below 100, a plateau model may represent the best approach to adjusting rating scale values for health-state scenarios when it is not feasible to elicit time-tradeoff utilities.
Touch-trigger probes are commonly used both in coordinate measuring machines (CMM) and in computer numerical control (CNC) machine tools. In both cases accuracy of measurement of the overall system and probing unit are closely interrelated. Key parameters of the probes are repeatability and pre-travel variation dependent on adjustable stylus force. To enable testing of the triggering force of the probes, the new setup was developed. The principle of the method and set-up is presented and its validity is experimentally confirmed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.