{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T02:56:21Z","timestamp":1781751381650,"version":"3.54.5"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2000,9,1]],"date-time":"2000-09-01T00:00:00Z","timestamp":967766400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2000,9,1]],"date-time":"2000-09-01T00:00:00Z","timestamp":967766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Scientific Computing"],"published-print":{"date-parts":[[2000,9]]},"DOI":"10.1023\/a:1011126400782","type":"journal-article","created":{"date-parts":[[2002,12,23]],"date-time":"2002-12-23T08:43:03Z","timestamp":1040632983000},"page":"293-322","source":"Crossref","is-referenced-by-count":37,"title":["A Hybrid Approach to Spectral Reconstruction of Piecewise Smooth Functions"],"prefix":"10.1007","volume":"15","author":[{"given":"Anne","family":"Gelb","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"297059_CR1","unstructured":"Banerjee, N. S., and Geer, J. (1995). Exponentially accurate approximations to piecewise smooth periodic functions, ICASE Report No. 95-17, NASA Langley Research Center."},{"key":"297059_CR2","unstructured":"Bateman, H. (1953). Higher Transcendental Functions, Vol. 2, McGraw-Hill."},{"key":"297059_CR3","unstructured":"Bauer, R. (1995). Band Filters for Determining Shock Locations, Ph.D. thesis, Applied Mathematics, Brown University."},{"issue":"4","key":"297059_CR4","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1137\/0729055","volume":"29","author":"W. Cai","year":"1992","unstructured":"Cai, W., Gottlieb, D., and Shu, C.-W. (1992). On one-sided filters for spectral Fourier approximations of discontinuous functions. SIAM J. Numer. Anal.\n29(4), 905\u2013916.","journal-title":"SIAM J. Numer. Anal."},{"key":"297059_CR5","doi-asserted-by":"crossref","unstructured":"Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1987). Spectral Methods in Fluid Dynamics.","DOI":"10.1007\/978-3-642-84108-8"},{"key":"297059_CR6","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1090\/S0025-5718-1995-1265014-7","volume":"64","author":"K. S. Eckhoff","year":"1995","unstructured":"Eckhoff, K. S. (1995). Accurate reconstructions of functions of finite regularity from truncated series expansions. Math. Comp.\n64, 671\u2013690.","journal-title":"Math. Comp."},{"key":"297059_CR7","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1090\/S0025-5718-98-00949-1","volume":"67","author":"K. S. Eckhoff","year":"1998","unstructured":"Eckhoff, K. S. (1998). On a high order numerical method for functions with singularities. Math. Comp.\n67, 1063\u20131087.","journal-title":"Math. Comp."},{"key":"297059_CR8","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1006\/acha.1999.0262","volume":"7","author":"A. Gelb","year":"1999","unstructured":"Gelb, A., and Tadmor, E. (1999). Detection of edges in spectral data. Appl. Comp. Harmonic Anal.\n7, 101\u2013135.","journal-title":"Appl. Comp. Harmonic Anal."},{"key":"297059_CR9","doi-asserted-by":"crossref","unstructured":"Gelb, A., and Tadmor, E. (2000). Detection of edges in spectral data II. Nonlinear enhan-cement. SIAM J. Numer. Anal. (in press).","DOI":"10.1137\/S0036142999359153"},{"key":"297059_CR10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0168-9274(99)00067-7","volume":"33","author":"A. Gelb","year":"2000","unstructured":"Gelb, A., and Tadmor, E. (2000). Enhanced spectral viscosity approximations for conser-vation laws. Appl. Numer. Math.\n33, 3\u201321.","journal-title":"Appl. Numer. Math."},{"key":"297059_CR11","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1109\/42.845180","volume":"19","author":"D. Gottlieb","year":"2000","unstructured":"Gottlieb, D., Gustafsson, B., and Forss\u00e9 n, P. (2000). On the direct Fourier method for computer tomography. IEEE Trans. Med. Imag.\n19, 223\u2013232.","journal-title":"IEEE Trans. Med. Imag."},{"key":"297059_CR12","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970425","volume-title":"Numerical Analysis of Spectral Methods: Theory and Applications","author":"D. Gottlieb","year":"1977","unstructured":"Gottlieb, D., and Orszag, S. (1977). Numerical Analysis of Spectral Methods: Theory and Applications, SIAM-CBMS, Philadelphia."},{"key":"297059_CR13","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1137\/S0036144596301390","volume":"39","author":"D. Gottlieb","year":"1997","unstructured":"Gottlieb, D., and Shu, C.-W. (1997). On the Gibbs phenomenon and its resolution. SIAM Rev.\n39, 644\u2013668.","journal-title":"SIAM Rev."},{"key":"297059_CR14","first-page":"1081","volume":"64","author":"D. Gottlieb","year":"1995","unstructured":"Gottlieb, D., and Shu, C.-W. (1995). On the Gibbs phenomenon IV. Recovering exponen-tial accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic func-tion. Math. Comp.\n64, 1081\u20131095.","journal-title":"Math. Comp."},{"key":"297059_CR15","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0377-0427(92)90260-5","volume":"43","author":"D. Gottlieb","year":"1992","unstructured":"Gottlieb, D., Shu, C.-W., Solomonoff, A., and Vandeven, H. (1992). On The Gibbs phenomenon I. Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function. J. Comput. Appl. Math.\n43, 81\u201392.","journal-title":"J. Comput. Appl. Math."},{"key":"297059_CR16","doi-asserted-by":"crossref","unstructured":"Gottlieb, D., and Tadmor, E. (1985). Recovering pointwise vales of discontinuous data within spectral accuracy. In Murman, E. M., and Abarbanel, S. S. (eds.), Progress and Supercomputing in Computational Fluid Dynamics, Proceedings of a 1984 U.S.-Israel Workshop, Progress in Scientific Computing, Vol. 6, Birkhauser, Boston, pp. 357\u2013375.","DOI":"10.1007\/978-1-4612-5162-0_19"},{"key":"297059_CR17","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1006\/jath.1997.3125","volume":"92","author":"G. Kvernadze","year":"1998","unstructured":"Kvernadze, G. (1998). Determination of the jump of a bounded function by its Fourier series. J. Approx. Theory\n92, 167\u2013190.","journal-title":"J. Approx. Theory"},{"key":"297059_CR18","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1137\/0730016","volume":"30","author":"Y. Maday","year":"1993","unstructured":"Maday, Y., Ould Kaber S. M., and Tadmor, E. (1993). Legendre pseudospectral viscosity method for nonlinear conservation laws. SIAM J. Numer. Anal.\n30, 321\u2013342.","journal-title":"SIAM J. Numer. Anal."},{"key":"297059_CR19","doi-asserted-by":"crossref","unstructured":"Mhaskar, H. N., and Prestin, J. (2000). On the detection of singularities of a periodic function, preprint.","DOI":"10.1023\/A:1018921319865"},{"key":"297059_CR20","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/BF02091780","volume":"10","author":"C.-W. Shu","year":"1995","unstructured":"Shu, C.-W., and Wong, P. (1995). A note on the accuracy of spectral method applied to nonlinear conservation laws. J. Sci. Comput.\n10, 357\u2013369.","journal-title":"J. Sci. Comput."},{"key":"297059_CR21","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1137\/0726003","volume":"26","author":"E. Tadmor","year":"1989","unstructured":"Tadmor, E. (1989). Convergence of spectral methods for nonlinear conservation laws. SIAM J. Numer. Anal.\n26, 30\u201344.","journal-title":"SIAM J. Numer. Anal."},{"key":"297059_CR22","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/BF01062118","volume":"48","author":"H. Vandeven","year":"1991","unstructured":"Vandeven, H. (1991). Family of spectral filters for discontinuous problems. SIAM J. Sci. Comput.\n48, 159\u2013192.","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1011126400782.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1011126400782\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1011126400782.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T13:22:02Z","timestamp":1751376122000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1011126400782"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["297059"],"URL":"https:\/\/doi.org\/10.1023\/a:1011126400782","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}