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A precise estimation method for locations in an inverse logarithmic potential problem for point mass models. (English) Zbl 0807.70003
Summary: A numerical method is discussed for an inverse logarithmic potential problem for a point mass model. We first show the relation between locations of point masses and Fourier expansion of the logarithmic potential, and show a method using discrete Fourier coefficients. Next a modified method is proposed based on a property of the discrete Fourier transform of the logarithmic potential. We give error estimates for our modified method, and compare it with the method using only discrete Fourier coefficients. Numerical examples illustrate the applicability and advantages of our modified method.

##### MSC:
 70F99 Dynamics of a system of particles, including celestial mechanics
##### Keywords:
Fourier expansion; discrete Fourier transform
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##### References:
  Anger, G., Inverse problems in differential equations, (1990), Plenum New York · Zbl 0752.35083  Yamaguti, M., Inverse problems in engineering sciences, (1991), Springer-Verlag Tokyo  Isakov, V., Inverse source problems, (1990), American Mathematical Society, Providence · Zbl 0721.31002  Kellogg, O.D., Foundations of potential theory, (1953), Dover New York · Zbl 0053.07301  Strakhov, V.N.; Brodsky, M.A., On the uniqueness of the inverse logarithmic potential problem, SIAM J. appl. math., 46, 324-344, (1986) · Zbl 0606.31001  Novikov, P., Sur le probléme inverse du potentiel, Dokl. akad. nauk SSSR, 18, 165-168, (1938), (in Russian) · JFM 64.0472.04  Smith, R.A., A uniqueness theorem concerning gravity fields, Proc. Cambridge philos. soc., 57, 865-870, (1961) · Zbl 0144.15501  Stromeyer, D.; Ballani, L., Uniqueness of the inverse gravimetric problem for point mass models, Manuscripta geodaetica, 9, 125-136, (1984) · Zbl 0541.31007  Ohnaka, K.; Uosaki, K., Boundary element approach for identification of point forces of distributed parameter systems, Int. J. control, 49, 119-127, (1989) · Zbl 0667.93024  Gardner, B.K.; Bernhard, R.J., A noise source identification technique using an inverse Helmholtz integral equation method, J. vib. acous. stress reliab. des., 110, 84-90, (1988)  Knuth, D.E., ()  Henrici, P., Applied and computational complex analysis, Vol. 1, (1974), John Wiley & Sons New York  Ohe, T. and Ohnaka, K. Determination of locations of point like masses in an inverse source problem of Poisson equation. J. Comput. Appl. Math. (in press) · Zbl 0821.65080  Smith, B.T., Error bounds for zeros of a polynomial based upon Gerschgorin’s theorem, J. ACM, 17, 661-674, (1970) · Zbl 0215.27305
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