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Evaluating the Influence of Data Type Precision On Numerical Algorithms
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Datum
2017
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Gesellschaft für Informatik e.V., Fachgruppe PARS
Zusammenfassung
IEEE 32 or 64 bit floating-point arithmetic is often sufficient for different kind of algorithms including scientific applications. However, there is a growing body of applications which have significant computational errors during the calculation leading to incorrect results. Such applications are ranging from numerical algorithms and probabilistic timing analysis to long-time simulations. While designing numerically stable algorithms or interval arithmetic pose possible solutions for certain problems, most scientific programmers are not aware of such deep numerical analyses. In addition, not all issues can be solved using above methods. High precision arithmetic, which is provided by software libraries or coprocessor designs, is a promising solution to overcome above numerical issues. Therefore, we investigate the influence of data type precision on a numerical algorithm, i.e. Lanczos algorithm, and compare different high precision arithmetic software libraries regarding accuracy and execution time. Additionally, we examine the usage of an exact scalar product for the Lanczos algorithm. While we show that high precision arithmetic is crucial for numerical algorithms, such arithmetic is still by far slower than hardware-supported data types.