History of Approximation Theory (HAT)

Articles on the History of Approximation Theory

The following are papers concerning various topics in the history of approximation theory. Some of these papers are linked. If you have problems with the links, please let us know. Some of these papers are given as pdf files. For them you will need an appropriate Adobe Acrobat reader which you probably have. Otherwise go to Adobe.

Akhiezer, N. I., Academician S. N. Bernstein and his Work on the Constructive Theory of Functions (in Russian), Izdat. Harkov. Gosudarstv. Univ., Kharkov, 1955; translated into German as Das Akademiemitglied S. N. Bernstein und seine Arbeiten zur konstruktiven Funktionentheorie, translated and with a preface by Ralitza K. Kovacheva and Heinz H. Gonska. in Mitt. Math. Sem. Giessen No. 240 (2000), xiv + 97 pages. The original is an expanded form of the survey paper by N. I. Akhiezer with the same title which appeared in Uspekhi Mat. Nauk (N.S.) 6 (1951), no. 1(41), 3-67, which was written by Akhieser on the occasion of Bernstein's 70th birthday.

Akhiezer, N. I., List of Publications. A list of publications of Naum Il'ich Akhiezer. We don't know how exact this list is.

Aleksandrov, P. S., Akhiezer, N. I., Gnedenko, B. V., and A. N. Kolmogorov, Sergei Natanovich Bernstein: Obituary, (in Russian) Uspekhi Mat. Nauk 24 (3) (1969), 211-218; translation in Russian Math. Surveys 24 (3) (1969), 169-176.

Andreev, A., Berdyshev, V. I., Bojanov, B., Kashin, B. S., Konyagin, S. V., Nikolskii, S. M., Oskolkov, K. I., Petrushev, P., Sendov, Bl., Telyakovskii, S. A., and V. N. Temlyakov, In memory of Sergei Borisovich Stechkin [1920-1995], East J. Approx. 2 (1996), 131-133.

Askey, R., In Memoriam. Antoni Zygmund (December 26, 1900 - May 30, 1992), J. Approx. Theory 71 (1992), 1-2.

Askey, R., Remembering Paul Turán, J. Approx. Theory 86 (1996), 253-254. For those with access, this article may be viewed at Science Direct.

Askey, R., and C. de Boor, In Memoriam: I. J. Schoenberg (1903-1990), J. Approx. Theory 63 (1990), 1-2. For those with access, this article may be viewed at Science Direct.

Askey, R. A., and P. Nevai, Gabor Szegö: 1895--1985, Math. Intelligencer 18 (1996), 10-22, and in Hungarian, Mat. Lapok 3 (1993), 13-32.

Babenko, Y., In Memoriam Anatolyi A. Ligun.

Babenko, V. F., Ligun, A. A., Motornyi, V. P., Nazarenko, N. A., and V. L. Velikin, In Memory of Nikolai Pavlovich Korneichuk.

Belinsky, E. S., List of Publications of Eduard S. Belinsky.

Boas, R. P., Extremal problems for polynomials, Amer. Math. Monthly 85 (1978), 473-475. A short pleasant expository note about the origins of the Markov inequality. This article may be viewed at JSTOR

Bogoljubov, A. N.; Grigorʹjan, A. T.; Drinfelʹd, G. I.; Juškevič, A. P., Ja. L. Geronimus (on the occasion of his seventy-fifth birthday), (Russian) Voprosy Istor. Estestvoznan. i Tehn. Vyp. 2(43) (1973), 71-72.

de Boor, C., and P. Nevai, In memoriam George G. Lorentz (1910-2006) , J. Approx. Theory 156 (2009), 1 - 27. For those with access, this article may be viewed at Science Direct.

de Boor, C., and A. Pinkus, The B-spline recurrence relations of Chakalov and Popoviciu, J. Approx. Theory 124 (2003), 115-123. This article may be viewed at Science Direct.

Borwein, P., and T. Erdélyi, Polynomials and Polynomial Inequalities, Springer-Verlag, New York, 1995. Contains a great deal of information on the history of approximation theory scattered throughout the text.

Brezinski, C., Historical Perspective on Interpolation, Approximation and Quadrature, in Handbook of Numerical Analysis, Volume III, eds. P. G. Ciarlet and J. L. Lions, p. 3-46, North Holland, 1994.

Bruins, E. M., On the history of approximation, in Constructive Function Theory '77, Sofia, 1980, 275-280.

Burkill, J. C., Charles-Joseph de la Vallée Poussin, J. London Math. Soc. 39 (1964), 165-175.

Butzer, P. L., An outline of the life and work of E. B. Christoffel (1829-1900), Historia Math. 8 (1981), 243-276.

Butzer, P., and F. Jongmans, P. L. Chebyshev (1821-1894), a guide to his life and work, J. Approx. Theory 96 (1999), 111-138. For those with access, this article may be viewed at Science Direct.

Butzer, P. L., and F. Jongmans, P. L. Chebyshev (1821-1894) and his contacts with Western European scientists, Historia Math. 16 (1989), 46-68.

Butzer, P. L., and R. J. Nessel, Aspects of de la Vallée Poussin's work in approximation and its influence, Archive Hist. Exact Sciences 46 (1993), 67-95.

Butzer, P. L., Schmidt, M. and E. L. Stark, Observations on the history of central B-splines, Archive Hist. Exact Sciences 39 (1988), 137-156.

Butzer, P. L., and E. L. Stark, The singular integral of Landau alias the Landau polynomials - Placement and impact of Landau's article ``Über die Approximation einer stetigen Funktion durch eine ganze rationale Funktion'', in Edmund Landau, Collected Works, Volume 3, eds. P. T. Bateman, L. Mirsky, H. L. Montgomery, W. Schall, I. J. Schoenberg, W. Schwarz, and H. Wefelscheid, 83-111, Thales-Verlag, Essen.

Butzer, P. L., and R. L. Stens, Sampling theory for not necessarily band-limited functions: a historical overview, SIAM Review 34 (1992), 40-53. This article may be viewed electronically at JSTOR.

Cheney, E. W., Introduction to Approximation Theory, McGraw-Hill Book Co., New York, 1966. The notes at the end of this book, pages 224-233, are especially recommended.

Cheney, E. W., and J. Levesley, In Memorium William Allan Light (1950-2002), J. Approx. Theory 123 (2003), 1-12. For those with access, this article may be viewed at Science Direct.

Dabrowski, K., and E. Hensz-Chadzynska, Józef Marcinkiewicz (1910-1940) in commemoration of the 60th anniversary of his death, in Fourier Analysis and Realted Topics, Banach Center Publications, Vol. 56, Polish Academy of Sciences, Warszawa, 2002. A ps file of this article can be found here.

Daepp, U, Gauthier, P., Gorkin, P., and G. Schmieder, Alice in Switzerland: The Life and Mathematics of Alice Roth, The Mathematical Intelligencer 27 (2005), 41-53.

Deutsch, F., The convexity of Chebyshev sets in Hilbert space, in Topics in Polynomials of One and Several Variables and Their Applications, eds. Th. M. Rassias, H. M. Srivastava, and A. Yanushauskas, World Scientific Publ. Co., 1993, 143-150. A brief historical account of work on the open question of whether every Chebyshev set in a Hilbert space must be convex.

Deutsch, F., Best Approximation in Inner Product Spaces, CMS Book in Mathematics, Springer-Verlag, New York, 2001. Each chapter ends with an interesting and useful section of ``Historical Notes''.

Dzyadyk, V. K., Mitropol'skii, Yu. A., and A. M. Samoilenko, Evgenii Yakovlevich Remez (on the centenary of his birth) (in Ukrainian), Ukrain. Mat. Zh. 48 (1996), 285-286.

Elliott, D., Lagrange interpolation -- decline and fall?, Internat. J. Math. Edu. Sci. Tech. 10 (1979), 1-12.

Erdelyi, T., and P. Vértesi, In Memoriam: Paul Erdős (1913-1996), J. Approx. Theory 94 (1998), 1-41. The article also contains a bibliography of Erdős' work in approximation theory compiled by J. Szabados. For those with access, this article may be viewed at Science Direct.

Erdős, P., Some notes on P. Turán's mathematical work, J. Approx. Theory 29 (1980), 2-5.

Freud, G., Publications of Geza Freud in approximation theory, J. Approx. Theory 46 (1986), 9-15. For a commentary on this list of publications see the following note by J. Szabados about the work of G. Freud.

Gasca, M., and T. Sauer, On the history of multivariate polynomial interpolation. Numerical analysis 2000, Vol. II: Interpolation and extrapolation, J. Comput. Appl. Math. 122 (2000), 23-35. This article may be viewed here, or alternatively, for those with access, this article may also be viewed at Science Direct

Gautschi, W., A survey of Gauss-Christoffel quadrature formulae, in E. B. Christoffel, The Influence of his Work on Mathematics and the Physical Sciences, eds. P. L. Butzer, F. Feher, 72-147, Birkhäuser, Basel, 1981.

Golinskii, Leonid, On the Scientific Legacy of Ya. L. Geronimus, Self-Similar Systems (Dubna, 1998), 273-281, Joint Inst. Nuclear Res., Dubna, 1999. An English translation by the author is here.

Goncharov, V. L., The Theory of Best Approximation of Functions, J. Approx. Theory 106 (2000), 2-57. This article, here translated into English, was originally published in 1945 in the collection The Scientific Heritage of P. L. Chebyshev. I. Mathematics, 122-172, Nauka. See also the commentary by V. M. Tikhomirov on pages 58-65 which follows the above article. For those with access, this article may be viewed at Science Direct. The commentary by V. M. Tikhomirov may be viewed at Science Direct.

Grünwald, G., List of Publications. Also available as a ps file.

Hart, W. L., Dunham Jackson, 1888-1946, Bull. Amer. Math. Soc. 54 (1946), 847-860.

Hsu, L. C., A survey of some recent developments of approximation theory in China, in Approximation theory, IV (College Station, Tex., 1983), eds. C. K. Chui, L. L. Schumaker and J. D. Ward, 123-151, Academic Press, New York, 1983.

Ivanov, K., and P. Petrushev, Curriculum vitae and list of publications of Prof. Vasil Atanasov Popov, Serdica Math. J. 28(4) (2002), ii-xvi.

Jakimovski, A. and J. Szabados, In Memoriam: Ambikeshwar Sharma (1920-2003), J. Approx. Theory 131 (2004), 1-18. For those with access, this article may be viewed at Science Direct.

Karlin, S., To I. J. Schoenberg and his mathematics, J. Approx. Theory 8 (1973), vi-ix.

Kotlyar, B. D., Nikolskii, S. M., Ponomarenko, V. G., Tikhomirov, V. M., Trofimov, V. N., Ulyanov, P. L., Aleksandr Filippovich Timan, (Russian) Uspekhi Mat. Nauk 44 (1989), no. 3(267), 145-146; translation in Russian Math. Surveys 44 (1989) no. 3, 179-180. The English translation of this article can be viewed at IOPScience.

Lacey M., Kolmogorov Entropy of the Mixed Derivative Spaces, (On Eduard Belinsky).

Liflyand E., Eduard Belinsky, His Life and Mathematics.

Lorentz, G. G., The work of P. Turán on interpolation and approximation, J. Approx. Theory 29 (1980), 6-10.

Lorentz, G. G., Superpositions, metric entropy, complexity of functions, widths, Bull. London Math. Soc. 22 (1990), 64-71. This is one of the articles within a series dedicated to the work of Andrei Nikolaevich Kolmogorov which appeared in Bull. London Math. Soc. 22 (1990), 31-100.

Lorentz, G. G., Antoni Zygmund and his work, J. Approx. Theory 75 (1993), 1-7. For those with access, this article may be viewed at Science Direct.

Lorentz, G. G., Mathematics and Politics in the Soviet Union from 1928 to 1953, J. Approx. Theory 116 (2002), 169-223. For those with access, this article may be viewed at Science Direct.

Lubinsky, D. S., Some personal recollections of Oved Shisha, J. Approx. Theory 86 (1996), 3-5. For those with access, this article may be viewed at Science Direct.

Marden, M., Homage to Walsh, J. Approx. Theory 5 (1972), ix-xiii.

Marden, M., Joseph L. Walsh in Memoriam, Bull. Amer. Math. Soc. 81 (1975), 45-65.

Meijering, E., A chronology of interpolation: From ancient astronomy to modern signal and image processing, Proceedings of the IEEE 90 (2002), 319-342.

Meinardus, G., and G. Nürnberger, In Memoriam: Lothar Collatz, J. Approx. Theory 65 (1991), 1-2. For those with access, this article may be viewed at Science Direct.

Meinardus, G., Nürnberger, G., Riessinger, Th., and G. Walz, The Work of Lothar Collatz in Approximation Theory, J. Approx. Theory 67 (1991), 119-128. For those with access, this article may be viewed at Science Direct.

Micchelli, C. A., On the work of Theodore J. Rivlin, in "The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin", Ann. Numer. Math. 4(1-4) (1997) viii-xiv.

Micchelli, C. A. and R. S. Varga, In Memoriam Theodore J. Rivlin (1926-2006), J. Approx. Theory 161 (2009), 1-8. For those with access, this article may be viewed at Science Direct.

Mitrpol'skii, Yu. A., Dzyadyk, V. K., and V. T. Gavrilyuk, Evgen'ii Yakovlevich Remez (on his 80th birthday), (in Russian) Ukrain. Mat. Zh. 28 (1976), 711; translation in Ukr. Math. J. 28 (1976), 553-554.

Mitrpol'skii, Yu. A., Dzyadyk, V. K., and V. T. Gavrilyuk, Evgen'ii Yakovlevich Remez (on the occasion of the ninetieth anniversary of his birth), (in Russian) Ukrain. Mat. Zh. 38 (1986), 539-540.

Nevai, P., Letter to a friend, J. Approx. Theory 46 (1986), 5-8. Biography of Geza Freud.

Nevai, P., Geza Freud, Orthogonal Polynomials and Christoffel Functions (A Case Study), J. Approx. Theory 48 (1986), 3-167.

Nürnberger, G., Professor Dr. Günter Meinardus celebrates his 80. birthday

Nürnberger, G., In memoriam Günter Meinardus (1926-2007), J. Approx. Theory, 162, 2010, 1-5, also includes a complete list of publications of Günter Meinardus.

Ortiz, E. L., and A. Pinkus, Herman Müntz: A Mathematician's Odyssey, The Mathematical Intelligencer 27 (2005), 22-31.

Pinkus, A., Weierstrass and Approximation Theory, J. Approx. Theory 107 (2000), 1-66. For those with access, this article may also be viewed at Science Direct. Some additions/corrections regarding this paper are in this file. This paper contains some biographical material, but is mainly concerned with the history of the Weierstrass Approximation Theorem. See also the interesting Veselý, J., Weierstrass' theorem before Weierstrass. A ps file of this article can be found here.

Révész, S., In Memoriam János Erőd

Schoenberg, I. J., List of Publications, essentially as it appears in I. J. Schoenberg, Selected Papers, ed. C. de Boor, Volume I, pp. xi-xviii, Birkhäuser, Boston, 1988. Also available as a ps file here.

Schoenberg, I. J., A brief account of my life and work, in I. J. Schoenberg, Selected Papers, ed. C. de Boor, Volume I, 1-10, Birkhäuser, Boston, 1988. Also available as a ps file here.

Sewell, W. E., Remarks on the mathematical researches of J. L. Walsh, SIAM J. Numer. Anal. 3 (1966), 344-348. This article may be viewed at JSTOR.

Shevchuk, I. A., On V. K. Dzjadyk's Investigations in Approximation Theory

Shisha, O., Publications of Oved Shisha, J. Approx. Theory 86 (1996), 6-12. For those with access, this article may be viewed at Science Direct.

Siegmund-Schultze, R., Der Beweis des Weierstrasschen Approximationssatzes 1885 vor dem Hintergrund der Entwicklung der Fourieranalysis (German) [The proof of Weierstrass' approximation theorem of 1885 against the background of the development of Fourier analysis], Historia Math. 15 (1988), 299-310.

Stone, M., A reminiscence on the extension of the Weierstrass approximation theorem, Historia Math. 3 (1976), 328.

Szabados, J., In Memoriam Arun Kumar Varma (1934-1994), J. Approx. Theory 84 (1996), 1-11. For those with access, this article may be viewed at Science Direct.

Szegö, G., Obituary: Otto Szász, Bull. Amer. Math. Soc. 60 (1954), 261-263.

Szegö, G., The contribution of L. Fejér to the constructive function theory, in Proceedings of the Conference on Constructive Theory of Functions, eds. G. Alexits and S. B. Stechkin, 19-26, Budapest, 1972.

Szüsz, P., P. Turán: Reminiscences of his student, J. Approx. Theory 29 (1980), 11-12.

Talbot, A., Approximation theory or a miss is better than a mile, Inaugural Lecture at University of Lancaster, 1970.

Tikhomirov, V. M., A. N. Kolmogorov and approximation theory, (in Russian) Uspekhi Mat. Nauk 44 (1989), 83-122; translation in Russian Math. Surveys 44 (1989), 101-152.

Tikhomirov, V. M., The papers of P. L. Chebyshev on approximation theory, (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 119 (1995), 86-90; translation in Moscow Univ. Math. Bull. 50 (1996), 39-42.

Todd, J., Applications of transformation theory: a legacy from Zolotarev (1847-1878), in Approximation theory and Spline Functions, eds. S. P. Singh, J. H. W. Burry, and B. Watson, 207-245, Reidel, Dordrecht, 1984.

Todd, J., A legacy from E. I. Zolotarev (1847-1878), Math. Intelligencer 10 (1988), 50-53.

Turán, P., Grünwald Géza élete és matematikai munkássaga, Matematikai Lapok 6 (1955), 6-26. An article, in Hungarian, about the life and work of Géza Grünwald.

Vlasov, V. F., Kolmogorov, A. N., Ponomarenko, V. G., Trofimov, V. N., Judin, D. B., Aleksandr Filippovic Timan (on the occasion of his sixtieth birthday). (Russian) Uspekhi Mat. Nauk 36 (1981), no. 2(218), 221-226.

Vértesi, P., In Memoriam--Lev Brutman (1939-2001), J. Approx. Theory 124 (2003), 1-6. For those with access, this article may be viewed at Science Direct.

Veselý, J., Weierstrass' theorem before Weierstrass. Some remarks of the development of ideas leading to the Weierstrass approximation theorem. Written for HAT. A ps file of this article can be found here.

Widder, D. V., Joseph Leonard Walsh, SIAM J. Numer. Anal. 3 (1966), 171-172. This article may be viewed electronically at JSTOR.

Wynn, P., The work of E. B. Christoffel on the theory of continued fractions, in E. B. Christoffel, The Influence of his Work on Mathematics and the Physical Sciences, eds. P. L. Butzer, F. Feher, 190-202, Birkhäuser, Basel, 1981.

Xu, Yuan, In Memoriam: Donald J. Newman (1930-2007), J. Approx. Theory 154 (2008), 37-58. For those with access, this article may be viewed at Science Direct.

Zalik, R. A., Tribute to Oved Shisha, J. Approx. Theory 86 (1996), 1-2. For those with access, this article may be viewed at Science Direct.

Back to the cover page