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A first category of methods relies on a direct interval evaluation of the given Chebyshev expansion in which Chebyshev polynomials are bounded, e.g., with a divide-and-conquer strategy. Our main category of methods that are based on the Clenshaw recurrence includes interval Clenshaw with defect correction (ICDC), and the spectral transformation of Clenshaw recurrence rewritten as a discrete dynamical system. An extension of the barycentric representation to interval arithmetic is also considered that has a log-linear complexity as it takes advantage of a verified discrete cosine transform. We compare different methods and provide illustrative numerical experiments. In particular, our eigenvalue-based methods are interesting for bounding the range of high-degree interval polynomials. Some of the methods rigorously compute narrow enclosures for high-degree Chebyshev expansions at thousands of points in a few seconds on an average computer. We also illustrate how to employ our methods as an automatic\n            <jats:italic>a posteriori<\/jats:italic>\n            forward error analysis tool to monitor the accuracy of the Chebfun feval command.\n          <\/jats:p>","DOI":"10.1145\/3319395","type":"journal-article","created":{"date-parts":[[2019,7,30]],"date-time":"2019-07-30T19:52:26Z","timestamp":1564516346000},"page":"1-33","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Enclosing Chebyshev Expansions in Linear Time"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8847-2058","authenticated-orcid":false,"given":"Behnam","family":"Hashemi","sequence":"first","affiliation":[{"name":"Shiraz University of Technology, Fars, Iran"}]}],"member":"320","published-online":{"date-parts":[[2019,7,30]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"G. Alefeld and J. Herzberger. 1983. 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