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Quasi-Monte Carlo for an Integrand with a Singularity Along a Diagonal in the Square

In: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Author

Listed:
  • Kinjal Basu

    (LinkedIn Inc.)

  • Art B. Owen

    (Stanford University)

Abstract

Quasi-Monte Carlo methods are designed for integrands of bounded variation, and this excludes singular integrands. Several methods are known for integrands that become singular on the boundary of the unit cube [0, 1]d or at isolated possibly unknown points within [0, 1]d. Here we consider functions on the square [0, 1]2 that may become singular as the point approaches the diagonal line x 1 = x 2, and we study three quadrature methods. The first method splits the square into two triangles separated by a region around the line of singularity, and applies recently developed triangle QMC rules to the two triangular parts. For functions with a singularity ‘no worse than |x 1 − x 2|−A is’ for 0

Suggested Citation

  • Kinjal Basu & Art B. Owen, 2018. "Quasi-Monte Carlo for an Integrand with a Singularity Along a Diagonal in the Square," Springer Books, in: Josef Dick & Frances Y. Kuo & Henryk Woźniakowski (ed.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pages 119-130, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-72456-0_6
    DOI: 10.1007/978-3-319-72456-0_6
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