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17 May 2022 A new type of spline interpolation method with its application in the tunneling process of tunnel boring machine
Jianjun Wan, Zhi Li, Hepei Zhang, Yuan Zhang, Shicang Song
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Proceedings Volume 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022); 1225945 (2022) https://doi.org/10.1117/12.2639240
Event: 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing, 2022, Kunming, China
Abstract
Considering the practice needed to calculate the curve curvature in the tunneling process of the tunnel boring machine, we design a scheme to construct a type of interpolating spline function. Under the weaker conditions that the original function fεC3 other than the usually C4 continuous, the error estimations are given between f and its interpolating spline S but their first two order derivatives as well. What showed method possesses optimal convergence order if either only fεC3 or ' f (x) can not be exactly given at endpoints. Applied this scheme, the curve curvature can be highly accurately determined.
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Jianjun Wan, Zhi Li, Hepei Zhang, Yuan Zhang, and Shicang Song "A new type of spline interpolation method with its application in the tunneling process of tunnel boring machine", Proc. SPIE 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 1225945 (17 May 2022); https://doi.org/10.1117/12.2639240
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KEYWORDS
Data modeling
Error analysis
Mathematics
Roads
Mathematical modeling
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