Abstract
An algorithm for computation of multivariate wavelet transforms on graphics processing units (GPUs) was proposed in [1]. This algorithm was based on the so-called isometric conversion between dimension and resolution (see [2] and the references therein) achieved by mapping the indices of orthonormal tensor-product wavelet bases of different number of variables and a tradeoff between the number of variables versus the resolution level, so that the resulting wavelet bases of different number of variables are with different resolution, but the overall dimension of the bases is the same.
In [1] we developed the algorithm only up to mapping of the indices of blocks of wavelet basis functions. This was sufficient to prove the consistency of the algorithm, but not enough for the mapping of the individual basis functions in the bases needed for a programming implementation of the algorithm. In the present paper we elaborate the full details of this ‘book-keeping’ construction by passing from block-matrix index mapping on to the detailed index mapping of the individual basis functions. We also consider some examples computed using the new detailed index mapping.
Research partially supported by the 2009, 2010 and 2011 Annual Research Grants of the Priority R&D Group for Mathematical Modeling, Numerical Simulation and Computer Visualization at Narvik University College, Norway.
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References
Dechevsky, L.T., Gundersen, J., Bang, B.: Computing n-Variate Orthogonal Discrete Wavelet Transforms on Graphics Processing Units. In: Lirkov, I., Margenov, S., Wasniewski, J. (eds.) LSSC 2009. LNCS, vol. 5910, pp. 730–737. Springer, Heidelberg (2010)
Dechevsky, L.T., Bang, B., Gundersen, J., Lakså, A., Kristoffersen, A.R.: Solving Non-linear Systems of Equations on Graphics Processing Units. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2009. LNCS, vol. 5910, pp. 719–729. Springer, Heidelberg (2010)
Cohen, A.: Wavelet methods in numerical analysis. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, vol. VII, pp. 417–712. Elsevier (2000)
Dechevsky, L.T.: Atomic decomposition of function spaces and fractional integral and differential operators. In: Rusev, P., Dimovski, I., Kiryakova, V. (eds.) Transform Methods and Special Functions, Part A. Fractional Calculus & Applied Analysis, vol. 2(4), pp. 367–381 (1999)
Dechevsky, L.T., Gundersen, J.: Isometric conversion between dimension and resolution. In: Dæhlen, M., Mørken, K., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces: Tromsø 2004, pp. 103–114. Nashboro Press, Brentwood TN (2005)
Dechevsky, L.T., Gundersen, J., Kristoffersen, A.R.: Wavelet-based isometic conversion between dimension and resolution and some of its applications. In: Proceedings of SPIE: Wavelet Applications in Industrial Processing V, Boston, Massachusetts, USA, vol. 6763 (2007)
Mallat, S.: A Wavelet Tour of Signal Processing, 2nd edn. Acad. Press (1999)
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Dechevsky, L.T., Bratlie, J., Gundersen, J. (2012). Index Mapping between Tensor-Product Wavelet Bases of Different Number of Variables, and Computing Multivariate Orthogonal Discrete Wavelet Transforms on Graphics Processing Units. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_45
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DOI: https://doi.org/10.1007/978-3-642-29843-1_45
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