Adaptive, self-validating numerical quadrature
SIAM Journal on Scientific and Statistical Computing
An efficient method for the numerical evaluation of partial derivatives of arbitrary order
ACM Transactions on Mathematical Software (TOMS)
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
Interval arithmetic and automatic error analysis in digital computing
Interval arithmetic and automatic error analysis in digital computing
Application of numerical interval analysis for statistical computing in a massively parallel computing environment
Interval arithmetic implementations: using floating point arithmetic
ACM SIGNUM Newsletter
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
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Conventional computations use real numbers as input and produce real numbers as results without any indication of the accuracy. Interval analysis, instead, uses interval elements throughout the computation and produces intervals as output with the guarantee that the true results are contained in them. One major use for interval analysis in statistics is to get results of high-dimensional multivariate probabilities. With the efforts to decrease the length of the intervals that contain the theoretically true answers, we can obtain results to any arbitrary accuracy, which is demonstrated by multivariate normal and multivariate t integrations. This is an advantage over the approximation methods that are currently in use. Since interval analysis is more computationally intensive than traditional computing, a MasPar parallel computer is used in this research to improve performance.