Error propagation in the Abel hill inverse problem
DOI:
https://doi.org/10.14419/ijamr.v12i1.32295Published:
2023-07-05Abstract
Abel’s Hill considers the problem of how to determine the shape of the hill from information on the return time of a rolled ball. Though this problem has been solved for piecewise monotonic functions, the issue of error propagation has not been addressed. This paper considers how errors in time measurement correlate to errors in determining the shape of the hill.
References
N. H. Abel, Resolution d'un probleme de mecanique, J. Reine Angew. Math., 1 (1826) 13-18.
M. Razavy, An Introduction to Inverse Problems in Physics, World Scientific, (2020), pp:6-15. https://doi.org/10.1142/11860.
J.B. Keller, Inverse Problems, Am. Math. Monthly, 83 (1976) 107-118. https://doi.org/10.1080/00029890.1976.11994053.
M.R.Spiegel, Mathematical Handbook of Formulas and Tables, McGraw-Hill, (1968), pp: 95.
