Extended introduction to algebraic interpolation
Matematičeskoe obrazovanie, no. 1 (2022), pp. 63-74 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper describes and justifies operators that allow one to find coefficients of interpolation polynomials and invert Vandermonde matrices. In addition, we give estimates for the complexity of these operators and questions of their software implementation are discussed.
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     author = {S. Soloviev},
     title = {Extended introduction to algebraic interpolation},
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S. Soloviev. Extended introduction to algebraic interpolation. Matematičeskoe obrazovanie, no. 1 (2022), pp. 63-74. http://geodesic.mathdoc.fr/item/MO_2022_1_a7/

[1] T. Kh. Kormen, Ch. I. Leizerson, R. L. Rivest, K. Shtain, Algoritmy: postroenie i analiz., ID Vilyams, M., 2005

[2] A. G. Sveshnikov, A. N. Tikhonov, Teoriya funktsii kompleksnoi peremennoi., Fizmatlit, M., 2010 | MR

[3] E. E. Tyrtyshnikov, Metody chislennogo analiza., ITs Akademiya, M., 2007

[4] E. E. Tyrtyshnikov, Osnovy algebry., Fizmatlit, M., 2017

[5] M. V. Ulyanov, Resursno-effektivnye kompyuternye algoritmy: razrabotka i analiz., Fizmatlit, M., 2008

[6] B. Beckermann, “The condition number of real Vandermonde, Krylov and positive definite Hankel matrices”, Numerische Mathematik., 85:4 (2000), 553–577 | DOI | MR | Zbl

[7] A. Borodin, I. Munro, The computational complexity of algebraic and numeric problems., American Elsevier Publishing Company, Inc., New York-London-Amsterdam, 1975 | MR | Zbl

[8] J. F. Traub, “Associated polynomials and uniform methods for the solution of linear problems”, SIAM Review., 7:3 (1966), 277–301 | DOI | MR

[9] L. N. Trefethen, Approximation Theory and Approximation Practice., SIAM, Oxford, UK, 2013 | MR | Zbl