Kronecker-product approximations for some function-related matrices

Linear Algebra and Its Applications

Volumn 379, Issue 1-3 SPEC. ISS, 2004, Pages 423-437

  Tyrtyshnikov, Eugene ^a  

^a INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

Asymptotically smooth functions; Kronecker product; Low rank matrices

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; FUNCTIONS; INTEGRAL EQUATIONS; THEOREM PROVING; WAVELET TRANSFORMS;

ASYMPTOTICALLY SMOTH FUNCTIONS; KRONECKER PRODUCT; LOW-RANK MATRICES;

MATRIX ALGEBRA;

EID: 0742320626     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2003.08.013     Document Type: Conference Paper

References (23)

1. Belotserkovsky S.M., Lifanov I.K. Method of Discrete Vortices. 1992;CRC Press.
2. Beylkin G., Mohlenkamp M.M. Numerical operator calculus in higher dimensions. PNAS. 99(16):2002;10246-10251.
3. Brandt A. Multilevel computations of integral transforms and particle interactions with oscillatory kernels. Comp. Phys. Commun. 65:1991;24-38.
4. De Lathauwer L., De Moor B., Vandewalle J. A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21(4):2000;1253-1278.
5. J.M. Ford, E.E. Tyrtyshnikov, Combining Kronecker product approximation with discrete wavelet transforms to solve dense, function-related systems, UMIST, Manchester Centre for Computational Mathematics, Numerical Analysis Report No. 418, 2003.
6. Goreinov S.A., Tyrtyshnikov E.E. The maximal-volume concept in approximation by low-rank matrices. Contemp. Math. 208:2001;47-51.
7. Goreinov S.A., Tyrtyshnikov E.E., Yeremin A.Y. Matrix-free iteration solution strategies for large dense linear systems. Numer. Linear Algebra Appl. 4(5):1996;1-22.
8. Goreinov S.A., Tyrtyshnikov E.E., Zamarashkin N.L. A theory of pseudo-skeleton approximations. Linear Algebra Appl. 261:1997;1-21.
9. Hackbusch W. A sparse matrix arithmetic based on. ℋ -matrices. I. Introduction to ℋ -matrices Computing. 62:1999;89-108.
10. Hackbusch W., Khoromskij B.N. A sparse. ℋ -matrix arithmetic. II. Application to multi-dimensional problems Computing. 64:2000;21-47.
11. W. Hackbusch, B.N. Khoromskij, E.E. Tyrtyshnikov, Hierarchical Kronecker tensor-product approximations, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Preprint No. 35, 2003.
12. Hackbusch W., Nowak Z.P. On the fast matrix multiplication in the boundary elements method by panel clustering. Numer. Math. 54(4):1989;463-491.
13. Ibraghimov I. Application of 3-way decomposition for matrix compression. Numer. Linear Algebra Appl. 9(6-7):2002;551-565.
14. Lifanov I.K. Singular Integral Equations and Disctrete Vortices. 1996;VSP.
15. Myagchilov M.V., Tyrtyshnikov E.E. A fast matrix-vector multiplier in discrete vortex method. Russian J. Numer. Anal. Math. Model. 7(4):1992;325-342.
16. Rokhlin V. Rapid solution of integral equations of classical potential theory. J. Comput. Phys. 60:1985;187-207.
17. Sun X., Pitsianis N.P. A matrix version of the fast multipole method. SIAM Rev. 43(2):2001;289-300.
18. Tyrtyshnikov E.E. Mosaic ranks and skeletons. Proceedings of WNAA-96. Lecture Notes in Computer Science 1196: Numerical Analysis and Its Applications. 1996;505-516 Springer-Verlag.
19. Tyrtyshnikov E.E. Mosaic-skeleton approximations. Calcolo. 33(1-2):1996;47-57.
20. Tyrtyshnikov E.E. Incomplete cross approximation in the mosaic-skeleton method. Computing. 64(4):2000;367-380.
21. Tyrtyshnikov E.E. Toeplitz matrices, some analogs and applications. (in Russian) Inst. Numer. Math., Rus. Acad. Sci. 1989.
22. Tyrtyshnikov E.E. A Brief Introduction to Numerical Analysis. 1997;Birkhäuser, Boston.
23. Van Loan C.F., Pitsianis N.P. Approximation with Kronecker products. NATO Adv. Sci. Ser. E Appl. Sci. vol. 232:1993;293-314 Kluwer, Dordrecht.