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We propose new nonpolynomial quadrature methods that avoid this effect by conformally mapping the usual ellipse of convergence to an infinite strip or another approximately straight-sided domain. The new methods are compared with related ideas of Bakhvalov, Kosloff and Tal-Ezer, Rokhlin and Alpert, and others. An advantage of the conformal mapping approach is that it leads to theorems guaranteeing geometric rates of convergence for analytic integrands. For example, one of the formulas presented is proved to converge $50\\%$ faster than Gauss quadrature for functions analytic in an $\\varepsilon$-neighborhood of $[-1,1]$.<\/jats:p>","DOI":"10.1137\/07068607x","type":"journal-article","created":{"date-parts":[[2008,3,5]],"date-time":"2008-03-05T19:23:53Z","timestamp":1204745033000},"page":"930-948","source":"Crossref","is-referenced-by-count":50,"title":["New Quadrature Formulas from Conformal Maps"],"prefix":"10.1137","volume":"46","author":[{"given":"Nicholas","family":"Hale","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lloyd N.","family":"Trefethen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,3,5]]},"reference":[{"key":"R1","unstructured":"M. Abramowitz and I. A. 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