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Interpolatorische Kubaturformeln

Seria
Rozprawy Matematyczne tom/nr w serii: 220 wydano: 1983
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Warianty tytułu
Abstrakty
DE

INNHALT
1. Einführung.......................................................................5
2. Allgemeine Darstellungssätze..........................................9
   2.1. Der Tschebyscheff-Rang endlicher Systeme.............9
   2.2. Darstellungssätze....................................................14
   2.3. Anwendungen..........................................................18
3. Polynomiale Theorie......................................................26
   3.1. Problemstellung.......................................................28
   3.2. Notwendige Eigenschaften interpolatorischer Kubaturformeln......33
   3.3. Reelle Ideale............................................................37
   3.4. Ein Charakterisierungssatz für interpolatorische Formeln.............40
4. Zweidimensionale Kubaturformeln.................................44
   4.1. Konstruktion reeller Ideale.......................................45
   4.2. Eine verbesserte Schranke für die Knotenanzahl....54
   4.3. Konstruktion von Formeln für Produktintegrale........59
5. Mehrdimensionale Kubaturformeln................................71
   5.1. Konstruktion reeller Ideale.......................................72
   5.2. Ein weiterer Charakterisierungssatz........................78
6. Beispiele........................................................................79
   6.1. Minimale Formeln bis zum Grad 9 für Produktintegrale.................81
   6.2. Integrale, für die minimale Formeln jedes Genauigkeitsgrades bekannt sind......87
   6.3. Nicht-minimale Formeln...........................................89
   6.4. Formeln für Integrale über dem Dreieck und dem Kreis................91
   6.5. Numerische Ergebnisse...........................................94
Literaturverzeichnis.........................................................120
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 220
Liczba stron
122
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXX
Daty
wydano
1983
Twórcy
Bibliografia
  • Albrecht, J. und L. Collatz [58] Zur numerischen Auswertung mehrdimensionaler Integrale. Z. Angew. Math. Mech. 38 (1958), 1-15.
  • Boltjanskii, V. G., S. S. Ryskov and Ju. A. Saskin [63] On k-regular imbeddings and their application to the theory of approximation of functions, Amer. Math. Soc. Translations (2) 28 (1963), 211-219.
  • Burnside. W. [08] An approximate quadrature formula. Messenger of Math. 37 (1908). 166-167.
  • Cernicina, V. Ja. [73] Construction of regions for which interpolation cubature formulas with the minimum number of nodes exist (in Russ.). Vestnik Leningrad. Univ. No. 1 (19731. 144-147.
  • Choquet, G. [69] Lectures on Analysis II. Representation Theory, W. A. Benjam, Inc., New York, Amsterdam 1969.
  • Davis, P. J. [67] A construction of nonnegative approximate quadratures, Math. Comp. 21 (1967), 578-587.
  • Davis, P.J. and P. Rabinowitz [67] Numerical Integration, Blaisdell, Walt ham, Mass., 1963.
  • Davis, P. J. and M. W. Wilson [68] Nonnegative interpolation formulas for uniformely elliptic equations, J. Approx. Theory 1 (1968), 374-380.
  • DeVore, R. A. [68] One-sided best approximation of functions, ibid. 1 (1968), 11-25.
  • Dubois, D. W. and G. Efroymson [70] Algebraic theory of real varieties I. In: Studies and essays presented to Yu-Why Chen on his sixtieth birthday, Taipei, Academia Sinica (1970), 107-135.
  • Efroymson, G. [74] Local reality on algebraic varieties, J. Algebra 29 (1974), 133-142.
  • Engels, H. [66] Neue Ergebnisse zur Numerischen Kubatur, Diss, Aachen 1966.
  • Engels, H. [80] Numerical Quadrature and Cubature, Academic Press, London, New York, Toronto, Sydney, San Francisco 1980.
  • Freud, G. [69] Orthogonale Polynome, Birkhäuser, Basel, Stuttgart 1969.
  • Fritsch, F. N. [70] On the existence of regions with minimal third degree integration formulas, Math. Comp. 24 (1970), 855-861.
  • Geyer, W.-D. [67] Anwendung der Modelltheorie in der algebraischen Geometrie, Tagungsbericht 12/67 einer Arbeitsgemeinschaft in Oberwolfach, Leitung: P. Roquette, 1967.
  • Haber, S. [70] Numerical evaluation of multiple integrals, Siam Review 12 (1970), 481-526.
  • Haegemans, A. and R. Piessens [76] Construction of cubature formulas of degree eleven for symmetric planar regions, using orthogonal polynomials, Numer. Math. 25 (1976), 139-148.
  • Haegemans, A. and R. Piessens [77] Construction of cubature formulas of degree seven and nine for symmetric planar regions, using orthogonal polynomials, Siam J. Numer. Anal. 14 (1977), 492-508.
  • Karlin, S. and W.J. Studden [66] Tschebycheff Systems: with Applications in Analysis and Statistics, Interscience, New York 1966.
  • Kroll, N., J. Linden und H. J. Schmid [80] Minimale Kubaturformeln für Integrale über dem Einheitsquadrat, Preprint No. 373 des Sonderforschungsbereiches 72 in Bonn 1980.
  • Kelley, J. L, I. N. Namioka et al. [63] Linear Topological Spaces, Van Nostrand Comp, Princeton, New Jersey, Toronto, London, Melbourne 1963.
  • Krylov V. I. [67] Approximative Berechnung von Integralen (in Russ.), Zweite Auflage, Moskau 1967.
  • Kuzmenkov, V, A. [76] The existence of cubature formulas with the least possible number of nodes (in Russ.), Zurn. vychisl. Math. nat. Fiz. 16 (1967), 242-245.
  • Mairhuber, J. C. [56] On Haar's theorem concerning Chebycheff problems having unique solutions, Proc. Amer. Math. Soc. 7 (1956), 609-615.
  • Macaulay, F. S. [16] The Algebraic Theory of Modular Systems, Cambridge Tracts in Math, and Math. Phys. No. 19, Cambridge Univ. Press, 1916.
  • Müller, H. M. [73] Polynomideale und Kubaturformeln, Diss, Univ. Dortmund, 1973.
  • Müller, H. M. [76] Kubaturformeln mit minimaler Knotenanzahl, Numer. Math. 25 (1976), 185-200.
  • Müller, H. M. [79] Lower bounds for the number of nodes in cubature formulas. In: Numerische Integration, Hrsgb. G. Hämmerlin, ISNM 45, 221-230, Birkhäuser, Basel, Boston, Stuttgart 1979.
  • Morrow, C. R. and T. N. L. Patterson [78] Construction of algebraic cubature rules using polynomial ideal theory, Siam J. Numer. Anal. 15 (1978), 953-976.
  • Müller, C. [62] Spherical Harmonics, Lecture Notes in Math. 17, Springer, Berlin, Heidelberg, New York 1962.
  • Mysovskikh, I. P. [64] On the construction of cubature formulas for the simplest regions (in Russ.), Zurn. vychisl. Mat. nat. Fiz. 4 (1964), 3-14.
  • Mysovskikh, I. P. [68] On the construction of cubature formulas with fewest knots, Soviet Math. Dokl. 9 (1968), 277-280.
  • Mysovskikh, I. P. [69] Cubature formulae and orthogonal polynomials. USSR Comp. Math. 9 (1969), 217-228.
  • Mysovskikh, I. P. [70] Numerical characteristics of orthogonal polynomials in two variables (in Russ.), Vestnik Leningrad. Univ. No. 19 (1970), Translated in: Vestnik Leningrad. Univ. Math. 3 (1976), 323-332.
  • Mysovskikh, 1. P. [73] Interpolatorische Kubaturformeln (in Russ.). In : Theorie von Kubaturformeln und Anwendung von Funktionalanalysi.s auf gewisse Probleme der Math. Physik, Hrsgb. S. L. Sobolev, Novosibirsk 1973, 73-90.
  • Mysovskikh, I. P. [75] On Chakalov's theorem, USSR Comp. Math. 15 (1975), 221-227.
  • Mysovskikh, I. P. [76] Orthogonale polynomials in several variables (in Russ.), Metody vychisl. 10, Izdvo Leningrad. Univ. (1976), 26-35.
  • Mysovskikh, I. P. [80] The approximation of multiple integrals by using interpolatory cubature formulae. In: Quantitative Approximation Theory, Eds. R. A. DeVore and K. Scherer, 217-243. Academic Press, New York, London, Sydney, Toronto, San Francisco 1980.
  • Mysovskikh, I. P. and V. Ja. Cernicina [71] The answer to a question of Radon, Soviet Math. Dokl. 12 (1971), 852-854.
  • Phillips, G. M. [67] Numerical integration in two and three dimensions. Computer J. 10 (1967), 202.
  • Radon, J. [48] Zur mechanischen Kubatur, Monatsh. Math. 52 (1948), 286-300.
  • Risler, J. J. [70] Une characterisation des idéaux des variétés algébriques réelles, Note aux CRAS, Paris 272 (1970), 1171-1173.
  • Risler, J. J. [74] Un théorème des zéroes en géométrie algébrique et analytique réelles. In: Fonctions de Plusieur Variables Complexes, Ed. F. Norguet, Lecture Notes in Math. 409 (1974), 522-531.
  • Rubinstein, G. S. [55] On a method of investigation of convex sets (in Russ.), Dokl. Akad. Nauk SSSR 102 (1955), 451-454.
  • Scbmid, H.J. [77] Interpolation of harmonic functions. In: Constructive Theory of Functions of Several Variables, Eds. W. Schempp und K. Zeller, Lecture Notes in Math. 571 (1977), 226-249.
  • Schmid, H. J. [78] On the representation of linear functional and the Tschebycheff-rank of finite systems. Preprint No. 174 of the SFB 72, Bonn 1978.
  • Schmid, H. J. [78]₂ On cubature formulae with a minimal number of knots, Numer. Math. 31 (1978), 282-297.
  • Schmid, H. J. [79] On cubature formulae of degree 2k-1. In: Numerische Integration, Hrsgb. G. Hammerlin, ISNM 45, 252-263, Birkhauser, Basel, Boston, Stuttgart 1979.
  • Schmid, H. J. [79]₂ Construction of cubature formulae using real ideals. In : Multivariate Approximation Theory, Eds. W. Schempp und K. Zeller, ISNM 51, 359-377, Birkhauser, Basel, Boston, Stuttgart 1979.
  • Schmid, H. J. [80] Kubaturformeln und reelle Ideate, Math. Z. 170 (1980), 267-282.
  • Schmid, H. J. [80]₂ On the numerical solution of non linear equations characterizing minimal cubature formulae, Computing 24 (1980), 251-257.
  • Shapiro, H. S. [71] Topics in approximation theory, Lecture Notes in Math. 187, 1971.
  • Stroud, A. H. [70] Approximate Calculation of Multiple Integrals, Prentice Hall, Englewood Cliffs, New Jersey, 1971.
  • Stroud, A. R, Kwan-Wei-Chen, Ping-Lei Wang und Zunkwang Mao [71] Some second and third degree harmonic interpolation formulas, Siam J. Numer. Anal. 8 (1971), 681-692.
  • Tschakaloff, V. [57] Formules de cubature mécaniques a coefficients non négatifs. Bull. Sci. Math. 12 (1957), 123-134.
  • Tyler, G. W. [53] Numerical integration of junctions of several variables, Canadian J. Math. 5 (1953), 493-512.
  • Whitney, H. [57] Elementary structure of real algebraic varietes, Ann. of Math. 66 (1957), 545-556.
  • Wilson, M. W. [69] A general algorithm for nonnegative quadrature formulas, Math. of Comp. 23 (1969), 253-258.
  • Zuhovickii, S. I. [62] On the approximation of real functions in the sense of P. L. Tschebyscheff, Amer. Math. Soc. Translations (2) 19 (1962), 221-252
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Identyfikator YADDA
bwmeta1.element.zamlynska-0e5f1c1b-8f4d-4ec3-ad07-7e7bef4c887c
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ISBN
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ISSN
0012-3862
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