Geodesic
Mosaic approximations of discrete analogs of Calder\'on--Zygmund operators
Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 81-94.

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Asymptotic estimates of the form $\operatorname{mr}A=O(\ln N\cdot\ln^d\varepsilon^{-1})$, where $d$ is the dimension of the initial space, for mosaic ranks of discrete analog of Calderón–Zygmund operators are obtained for various mosaic covers. 
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N. É. Mikhailovskii. Mosaic approximations of discrete analogs of Calder\'on--Zygmund operators. Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 81-94. http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a8/

[1] Voevodin V. V., Tyrtyshnikov E. E., Vychislitelnye protsessy s teplitsevymi matritsami, Nauka, M., 1988 | Zbl

[2] Lifanov I. K., Tyrtyshnikov E. E., “Teplitsevy matritsy i singulyarnye integralnye uravneniya”, Vychislitelnye protsessy i sistemy, no. 7, ed. G. I. Marchuk, Nauka, M., 1989

[3] Tyrtyshnikov E. E., Teplitsevy matritsy, nekotorye ikh analogi i prilozheniya, OVM AN SSSR, M., 1989

[4] Rokhlin V., “Rapid solution of integral equations of classical potential theory”, J. Comput. Phys., 60 (1985), 187–207 | DOI | MR | Zbl

[5] Rokhlin V., “Rapid solution of integral equations of scattering theory in two dimensions”, J. Comput. Phys., 86 (1990), 414–439 | DOI | MR | Zbl

[6] Carrier J., Greengard L., Rokhlin V., “A fast adaptive multipole algorithm for particle simulations”, SIAM J. Sci. Comput., 9 (1988), 669–686 | DOI | MR | Zbl

[7] Engheta N., Murphy W. D., Rokhlin V., Vassiliou M. S., “The fast multipole method (FMM) for electromagnetic scattering problems”, IEEE Trans. Antennas and Propagation, 40:6 (1992), 634–641 | DOI | MR | Zbl

[8] Greengard L., Rokhlin V., “A fast algorithm for particle simulations”, J. Comput. Phys., 73 (1990), 325–348 | DOI | MR

[9] Nechepurenko Yu. M., Bystrye chislenno ustoichivye algoritmy dlya shirokogo klassa lineinykh diskretnykh preobrazovanii, Preprint No. 92, OVM AN SSSR, M., 1985

[10] Brandt A., Lubrecht A. A., “Multilevel matrix multiplication and fast solution of integral equations”, J. Comput. Phys., 90 (1990), 348–370 | DOI | MR | Zbl

[11] Novak Z. P., Khakbush U., “O slozhnosti metoda panelei”, Vychislitelnye protsessy i sistemy, no. 6, ed. G. I. Marchuk, Nauka, M., 1988

[12] Hackbush W., Nowak Z. P., “On the Fast Matrix Multiplication in the Boundary Element Method by Panel Clustering”, Numer. Math., 59 (1989), 463–491 | DOI

[13] Tyrtyshnikov E. E., “Mosaic ranks and skeletons”, Lecture Notes in Comput. Sci., 1196, 1997, 505–516 | MR

[14] Beylkin G., Coifman R., Rokhlin V., “Fast wavelet transforms and numerical algorithms, I”, Comm. Pure Appl. Math., 44 (1991), 141–183 | DOI | MR | Zbl

[15] Goreinov S. A., Tyrtyshnikov E. E., Zamarashkin N. L., “Pseudo-skeleton approximations”, Linear Algebra Appl. (to appear)

[16] Marchuk G. I., Agoshkov V. I., Vvedenie v proektsionno-setochnye metody, Nauka, M., 1981

[17] Brebbiya K., Telles Zh., Vroubel L., Metody granichnykh elementov, Mir, M., 1987

[18] Egorov Yu. V., Lineinye differentsialnye uravneniya glavnogo tipa, Nauka, M., 1984