Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Numerical Indefinite Integration of Functions with Singularities

Aeyoung Park Jang and Seymour Haber
Mathematics of Computation
Vol. 70, No. 233 (Jan., 2001), pp. 205-221
Stable URL: http://www.jstor.org/stable/2698930
Page Count: 17
  • Read Online (Free)
  • Download ($34.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Numerical Indefinite Integration of Functions with Singularities
Preview not available

Abstract

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for Hp functions, for p > 1, over the interval (-1, 1). The main factor in the error of our indefinite quadrature formula is O(e$^{- \pi \sqrt {N/q}}$), with 2N nodes and 1/p + 1/q = 1. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of $\sqrt {2}$ in the constant of the exponential. We conjecture that our formula has the best possible value for that constant. The results of numerical examples show that our indefinite quadrature formula is better than Haber's indefinite quadrature formula for Hp-functions.

Page Thumbnails

  • Thumbnail: Page 
205
    205
  • Thumbnail: Page 
206
    206
  • Thumbnail: Page 
207
    207
  • Thumbnail: Page 
208
    208
  • Thumbnail: Page 
209
    209
  • Thumbnail: Page 
210
    210
  • Thumbnail: Page 
211
    211
  • Thumbnail: Page 
212
    212
  • Thumbnail: Page 
213
    213
  • Thumbnail: Page 
214
    214
  • Thumbnail: Page 
215
    215
  • Thumbnail: Page 
216
    216
  • Thumbnail: Page 
217
    217
  • Thumbnail: Page 
218
    218
  • Thumbnail: Page 
219
    219
  • Thumbnail: Page 
220
    220
  • Thumbnail: Page 
221
    221