Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IM2_1996_60_5_a6, author = {O. V. Matveev}, title = {Methods of approximate reconstruction of functions defined on chaotic lattices}, journal = {Izvestiya. Mathematics }, pages = {985--1025}, publisher = {mathdoc}, volume = {60}, number = {5}, year = {1996}, language = {en}, url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a6/} }
O. V. Matveev. Methods of approximate reconstruction of functions defined on chaotic lattices. Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 985-1025. http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a6/
[1] Sharma A., Meir A., “Degree of approximation of spline interpolation”, J. Math. Mech., 15:5 (1966), 759–767 | MR | Zbl
[2] Nord S., “Approximation properties of the spline fit”, BIT, 7:2 (1967), 132–144 | DOI | MR | Zbl
[3] Farwig R., “Rate of convergence of Shepard's global interpolation formula”, Math. Comput., 46:174 (1986), 577–590 | DOI | MR | Zbl
[4] Matveev O. V., “Approksimativnye svoistva interpolyatsionnykh $D^m$-splainov”, DAN SSSR, 321:1 (1991), 14–18 | MR | Zbl
[5] Matveev O. V., “Splain-interpolyatsiya funktsii neskolkikh peremennykh i bazisy v prostranstvakh Soboleva”, Tr. MIRAN, 198 (1992), 125–152 | MR | Zbl
[6] Schumaker L. L., “Fitting surfaces to scattered data”, Approximation theory, II, Acad. Press, N. Y., 1976, 203–268 | MR
[7] Alberg Dzh., Nilson E., Uolsh Dzh., Teoriya splainov i ee prilozheniya, Mir, M., 1972 | MR | Zbl
[8] Mansfield L. E., “On the optimal approximation of linear functionals in spaces of bivariate functions”, SIAM J. Numer. Anal., 8:1 (1971), 115–126 | DOI | MR | Zbl
[9] Mansfield L. E., “On the variational characterization and convergence of bivariate splines”, Numer. Math., 20:2 (1972), 99–114 | DOI | MR | Zbl
[10] Mansfield L. E., “Optimal approximation and error bounds in spaces of bivariate functions”, J. Appr. Theory, 5:1 (1972), 77–96 | DOI | MR | Zbl
[11] Loran P.-Zh., Approksimatsiya i optimizatsiya, Mir, M., 1975
[12] Nielson G. M., “Bivariate spline functions and the approximation of linear functionals”, Numer. Math., 21:2 (1973), 138–160 | DOI | MR | Zbl
[13] Nielson G. M., “Multivariate smoothing and interpolating splines”, SIAM J. Numer. Anal., 11:2 (1974), 435–446 | DOI | MR | Zbl
[14] Mansfield L. E., “On the variational approach to defining splines on $L$-shaped regions”, J. Appr. Theory, 12:2 (1974), 99–112 | DOI | MR | Zbl
[15] Mansfield L. E., “Error bounds for spline interpolation over rectangular polygons”, J. Appr. Theory, 12:2 (1974), 113–126 | DOI | MR | Zbl
[16] Zavyalov Yu. S., Kvasov B. I., Miroshnichenko V. L., Metody splain-funktsii, Nauka, M., 1980 | MR
[17] Birkhoff G., Schultz M. H., Varga R. S., “Piecewise Hermite interpolation in one and two variables with applications to partial differential equations”, Numer. Math., 11:3 (1968), 232–256 | DOI | MR | Zbl
[18] Bramble J. H., Zlámal M., “Triangular elements in the finite element method”, Math. Comput., 24:112 (1970), 809–820 | DOI | MR
[19] Zlámal M., “A finite element procedure of the second order of accuracy”, Numer. Math., 14:4 (1970), 394–402 | DOI | MR | Zbl
[20] Gordon W. J., “Blending-function methods of bivariate and multivariate interpolation and approximation”, SIAM J. Numer. Anal., 8:1 (1971), 158–177 | DOI | MR | Zbl
[21] Nicolaides R. S., “On the class of finite elements generated by Lagrange interpolation”, SIAM J. Numer. Anal., 9:3 (1972), 435–445 | DOI | MR | Zbl
[22] Nicolaides R. A., “On the class of finite elements generated by Lagrange interpolation, II”, SIAM J. Numer. Anal., 10:1 (1973), 182–189 | DOI | MR | Zbl
[23] Zlámal M., “Curved elements in the finite element method, I”, SIAM J. Numer. Anal., 10:1 (1973), 229–240 | DOI | MR | Zbl
[24] Barnhill R. E., Birkhoff G., Gordon W. J., “Smooth interpolation in triangles”, J. Appr. Theory, 8:2 (1973), 114–128 | DOI | MR | Zbl
[25] Barnhill R. E., Gregory J. A., “Compatible smooth interpolation in triangles”, J. Appr. Theory, 15:3 (1975), 214–225 | DOI | MR | Zbl
[26] McLain D. H., “Two dimensional interpolation from random data”, Comput. J., 19:2 (1976), 178–181 | MR | Zbl
[27] Nielson G., “Minimum norm interpolation in triangles”, SIAM J. Numer. Anal., 17:1 (1980), 44–62 | DOI | MR | Zbl
[28] Franke R., “Scattered data interpolation: tests of some methods”, Math. Comput., 38:157 (1982), 181–200 | DOI | MR | Zbl
[29] Maude A. D., “Interpolation – mainly for graph plotters”, Comput. J., 16:1 (1973), 64, 65 | DOI | Zbl
[30] Franke R., “Locally determined smooth interpolation at irregularly spaced points in several variables”, J. Inst. Math. Appl., 19:4 (1977), 471–482 | DOI | MR | Zbl
[31] Franke R., “Smooth interpolation of scattered data by local thin plate splines”, Comput. Math., 8:4 (1982), 273–281 | MR | Zbl
[32] Shepard D., “A two-dimensional interpolation function for irregularly-spaced data”, Proc. 23rd ACM Nat. Conf., Princeton–N. Y.– London, 1968, 517–524
[33] Gordon W. J., Wixom J. A., “Shepard's method of “metric interpolation” to bivariate and multivariate interpolation”, Math. Comput., 32:141 (1978), 253–264 | DOI | MR | Zbl
[34] McLain D. H., “Drawing contours from arbitrary data points”, Comput. J., 17:4 (1974), 318–324
[35] Lancaster P., “Moving weighted least-squares methods”, Polynomial and spline approximation, Reidel, Dordrecht, 1979, 103–120 | MR
[36] Foley T. A., “Full Hermite interpolation to multivariate scattered data”, Approximation theory, IV, Acad. Press, N. Y., 1983, 465–470 | MR
[37] Nielson G. M., “Coordinate free scattered data interpolation”, Topics in multivariate approximation, Acad. Press, N. Y., 1987, 175–184 | MR
[38] Duchon J., “Splines minimizing rotation-invariant semi-norms in Sobolev spaces”, Lect. Notes Math., 571 (1977), 85–100 | DOI | MR | Zbl
[39] Franke R., “Recent advances in the approximation of surfaces from scattered data”, Topics in multivariate approximation, Acad. Press, N. Y., 1987, 79–98 | MR
[40] Madych W. R., Nelson S. A., “Multivariate interpolation and conditionally positive definite functions”, Appr. Theory Appl., 4:4 (1988), 77–89 | MR | Zbl
[41] Dyn N., Light W. A., Cheney E. W., “Interpolation by piecewise-linear radial basis functions”, J. Appr. Theory, 59:2 (1989), 202–223 | DOI | MR | Zbl
[42] Light W. A., Cheney E. W., “Interpolation by piecewise-linear radial basis functions, II”, J. Appr. Theory, 64:1 (1991), 38–54 | DOI | MR | Zbl
[43] Narcowich F. J., Ward J. D., “Norms of inverses and condition numbers for matrices associated with scattered data”, J. Appr. Theory, 64:1 (1991), 69–94 | DOI | MR | Zbl
[44] Atteia M., “Existence et détermination des fonctions “spline” à plusieurs variables”, C. R. Acad. Sci. Paris. Sér. A, 262:10 (1966), 575–578 | MR | Zbl
[45] Stechkin S. B., Subbotin Yu. N., Splainy v vychislitelnoi matematike, Nauka, M., 1976 | MR | Zbl
[46] Duchon J., “Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces”, RAIRO. Anal. Numér, 10:12 (1976), 5–12 | MR
[47] Duchon J., “Sur l'erreur d'interpolation des finctions de plusieurs variables par les $D^m$-splines”, RAIRO. Anal. Numér, 12:4 (1978), 325–334 | MR | Zbl
[48] Meinguet J., “An intrinsic approach to multivariate spline interpolation at arbitrary points”, Polynomial and spline approximation, Reidel, Dordrecht, 1979, 163–190 | MR
[49] Vasilenko V. A., Splain-funktsii: teoriya, algoritmy, programmy, Nauka, Novosibirsk, 1983 | MR
[50] Goodman T. N. T., Lee S. L., “Cardinal interpolation by $D^m$-splines”, Proc. Roy. Soc. Edinburgh, 94A:1,2 (1983), 149–161 | MR
[51] Korneichuk N. P., Splainy v teorii priblizheniya, Nauka, M., 1984 | MR
[52] Bezhaev A. Yu., $D^m$-splainy v zadachakh priblizheniya funktsii na khaoticheskikh setkakh, Avtoref. dis. ... kand. fiz.-mat. nauk, VTs SO AN SSSR, Novosibirsk, 1985
[53] Shadrin A. Yu., “O priblizhenii funktsii interpolyatsionnymi splainami, zadannymi na neravnomernykh setkakh”, Matem. sb., 181:9 (1990), 1236–1255
[54] Madych W. R., Nelson S. A., “Polyharmonic cardinal splines”, J. Appr. Theory, 60:2 (1990), 141–156 | DOI | MR | Zbl
[55] Madych W. R., Nelson S. A., “Polyharmonic cardinal splines: a minimization property”, J. Appr. Theory, 63:3 (1990), 303–320 | DOI | MR | Zbl
[56] Vitushkin A. G., Otsenka slozhnosti zadachi tabulirovaniya, Fizmatgiz, M., 1959
[57] Rosen J. B., “Minimum error bounds for multidimensional spline approximation”, J. Comput. Syst. Sci., 5:4 (1971), 430–452 | DOI | MR | Zbl
[58] Zwart P. B., “Multivariate splines with nondegenerate partitions”, SIAM J. Numer. Anal., 10:4 (1973), 665–673 | DOI | MR | Zbl
[59] Hayes J. G., Halliday J., “The least-squares fitting of cubic spline surfaces to general data sets”, J. Inst. Math. Appl., 14:1 (1974), 89–103 | DOI | MR | Zbl
[60] Kaufman E. H., Taylor G. D., “Uniform rational approximation of functions of several variables”, Int. J. Numer. Math. Eng., 9:2 (1975), 297–323 | DOI | MR | Zbl
[61] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR
[62] Matveev O. V., “O nekotorykh metodakh vosstanovleniya funktsii $n$ peremennykh, zadannykh na khaoticheskikh setkakh”, Dokl. RAN, 326:4 (1992), 605–609 | Zbl
[63] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl
[64] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR
[65] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1984 | MR | Zbl
[66] Ikramov Kh. D., “Iteratsionnye metody”, Matem. entsiklopediya, T. 2, Sov. entsiklopediya, M., 1979, 686–689
[67] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | MR
[68] Subbotin Yu. N., “Zavisimost otsenok mnogomernoi kusochno-polinomialnoi approksimatsii ot geometricheskikh kharakteristik triangulyatsii”, Tr. MIAN SSSR, 189, Nauka, M., 1989, 117–137 | MR