Fast and Numerically Stable Approximate Solution of Trummer’s Problem

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References

[1] Rokhlin, V. (1985) Rapid Solution of Integral Equations of Classical Potential Theory. Journal of Computational Physics, 60, 187-207. http://dx.doi.org/10.1016/0021-9991(85)90002-6

[2] Gerasoulis, A. (1987) A Fast Algorithm for the Multiplication of Generalized Hilbert Matrices with Vectors. Mathematics of Computation, 50, 179-188. http://dx.doi.org/10.1090/S0025-5718-1988-0917825-9

[3] Greengard, L. and Rokhlin, V. (1987) A Fast Algorithm for Practice Simulation. Journal of Computational Physics, 73, 325-348. http://dx.doi.org/10.1016/0021-9991(87)90140-9

[4] Pan, V.Y., Zheng, A., Huany, X. and Yu, Y. (1995) Fast Multipoint Polynomial Evaluation and Interpolation via Computation with Structured Matrices. Annals of Numerical Mathematics, 4, 483-510.

[5] Pan, V.Y. (2001) Structured Matrices and Polynomials, Unified Superfast Algorithms. Birkhauser, Boston.

http://dx.doi.org/10.1007/978-1-4612-0129-8

[6] Bini, D. and Pan, V.Y. (1994) Polynomial and Matrix Computations, Volume 1: Fundamental Algorithms. Birkhauser, Boston. http://dx.doi.org/10.1007/978-1-4612-0265-3

[7] Pan, V.Y., Tabanjeh, M., Chen, Z., Landowne, E. and Sadikou, A. (1998) New Transformations of Cauchy Matrices and Trummer’s Problem. Computers & Mathematics with Applications, 35, 1-5.

http://dx.doi.org/10.1016/S0898-1221(98)00091-1

[8] Fink, T., Heinig, G. and Rost, K. (1993) An Inversion Formula and Fast Algorithms for Cauchy-Vandermonde Matrices. Linear Algebra & Its Applications, 183, 179-191. http://dx.doi.org/10.1016/0024-3795(93)90431-M

[9] Pan, V.Y., Landowne, E., Sadikou, A. and Tiga, O. (1993) A New Approach to Fast Polynomial Interpolation and Multipoint Evaluation. Computers & Mathematics with Applications, 25, 25-30.

http://dx.doi.org/10.1016/0898-1221(93)90129-J

[10] Pan, V.Y. (1995) An Algebraic Approach to Approximate Evaluation of a Polynomial on a Set of Real Points. Advances in Computational Mathematics, 3, 41-58. http://dx.doi.org/10.1007/BF02431995