Algorithms for verified inclusions—theory and practice
Reliability in computing: the role of interval methods in scientific computing
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Interval Newton/generalized bisection when there are singularities near roots
Annals of Operations Research
Interval analysis: theory and applications
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Digital Alias-free Signal Processing
Digital Alias-free Signal Processing
Introduction to Interval Analysis
Introduction to Interval Analysis
Information science: On the choice of sampling rates in parametric identification of time series
Information Sciences: an International Journal
Validated Numerics: A Short Introduction to Rigorous Computations
Validated Numerics: A Short Introduction to Rigorous Computations
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This paper shows that the uncertainty due to derivation of fluxes from integral model input can be at least as large as that due to uncertainty in the measurements. The method used to illustrate the problem is interval arithmetic. During calibration hydrological models often seem to perform equally well for two or more sets of parameters that differ considerably. There are many ingredients that may contribute to this. One of those ingredients is a mismatch of information present in input and output data and information used by the model. In this paper we examine one particular case where this occurs. We assume that the input data sets are time series of fluxes integrated over fixed or variable time intervals, while outputs can be the result of continuous or discrete, direct or indirect flux measurements. We assume that for model calibration purposes each output value represents a value at a specific point in time. We show that even for a linear reservoir the process of averaging and sampling may make recovery of its sole parameter impossible. We also show that these problems can be diagnosed and for this simple model also solved through the use of interval arithmetic.