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The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.<\/jats:p>","DOI":"10.1007\/s11075-020-01057-7","type":"journal-article","created":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T01:03:01Z","timestamp":1609808581000},"page":"793-811","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Barycentric prolate interpolation and pseudospectral differentiation"],"prefix":"10.1007","volume":"88","author":[{"given":"Yan","family":"Tian","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,1,5]]},"reference":[{"issue":"3","key":"1057_CR1","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1137\/S0036144502417715","volume":"46","author":"J Berrut","year":"2004","unstructured":"Berrut, J., Trefethen, L.: Barycentric lagrange interpolation. 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