{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:08:54Z","timestamp":1759838934981},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,4,25]],"date-time":"2013-04-25T00:00:00Z","timestamp":1366848000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2013,12]]},"DOI":"10.1007\/s10915-013-9717-9","type":"journal-article","created":{"date-parts":[[2013,5,1]],"date-time":"2013-05-01T04:37:25Z","timestamp":1367383045000},"page":"502-517","source":"Crossref","is-referenced-by-count":1,"title":["Iterated Fast Collocation Methods for Integral Equations of the Second Kind"],"prefix":"10.1007","volume":"57","author":[{"given":"Zhongying","family":"Chen","sequence":"first","affiliation":[]},{"given":"Guangqing","family":"Long","sequence":"additional","affiliation":[]},{"given":"Gnaneshwar","family":"Nelakanti","sequence":"additional","affiliation":[]},{"given":"Yongdong","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,4,25]]},"reference":[{"key":"9717_CR1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511626340","volume-title":"The Numerical Solution of Integral Equations of the Second Kind","author":"KE Atkinson","year":"1997","unstructured":"Atkinson, K.E.: The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, Cambridge (1997)"},{"key":"9717_CR2","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1137\/0720012","volume":"20","author":"KE Atkinson","year":"1983","unstructured":"Atkinson, K.E., Graham, I.G., Sloan, I.: Piecewise continuous collocation for integral equations. SIAM J. Numer. Anal. 20, 172\u2013186 (1983)","journal-title":"SIAM J. Numer. Anal."},{"key":"9717_CR3","volume-title":"Sobolev Spaces","author":"RA Adams","year":"2003","unstructured":"Adams, R.A., Fournier, J.: Sobolev Spaces, 2nd edn. Academic Press, New York (2003)","edition":"2"},{"key":"9717_CR4","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1002\/cpa.3160440202","volume":"44","author":"G Beylkin","year":"1991","unstructured":"Beylkin, G., Coifman, R., Rokhlin, V.: Fast wavelet transforms and numerical algorithms I. Commun. Pure Appl. Math. 44, 141\u2013183 (1991)","journal-title":"Commun. Pure Appl. Math."},{"key":"9717_CR5","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1070\/SM1970v011n02ABEH002065","volume":"11","author":"JA Brudnyi","year":"1970","unstructured":"Brudnyi, J.A.: A multidimensional analogue of a theorem of Whitney. Iath. USSR Sb. 11, 157\u2013170 (1970)","journal-title":"Iath. USSR Sb."},{"key":"9717_CR6","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1216\/jiea\/1181075816","volume":"6","author":"Y Cao","year":"1994","unstructured":"Cao, Y., Xu, Y.: Singular preserving Galerkin methods for weakly singular Fredholm integral equations. J. Integral Equ. Appl. 6, 303\u2013334 (1994)","journal-title":"J. Integral Equ. Appl."},{"key":"9717_CR7","doi-asserted-by":"crossref","unstructured":"Chen, M., Chen, Z., Chen, G.: Approximate Solutions of Operator Equation. World Scientific Publishing Co., Singapore (1997)","DOI":"10.1142\/3407"},{"key":"9717_CR8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/A:1018994802659","volume":"7","author":"Z Chen","year":"1997","unstructured":"Chen, Z., Micchelli, C.A., Xu, Y.: The Petrov-Galerkin methods for second kind integral equations II: multiwavelet scheme. Adv. Comput. Math. 7, 199\u2013233 (1997)","journal-title":"Adv. Comput. Math."},{"key":"9717_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1014273420351","volume":"16","author":"Z Chen","year":"2002","unstructured":"Chen, Z., Micchelli, C.A., Xu, Y.: Discrete wavelet Petrov-Galerkin methods. Adv. Comput. Math. 16, 1\u201328 (2002)","journal-title":"Adv. Comput. Math."},{"key":"9717_CR10","unstructured":"Chen, Z., Micchelli, C.A., Xu, Y.: Fast collocation methods for second kind integral equations. SIAM J. Numer. Anal. 40, 344\u2013375 (2002)"},{"key":"9717_CR11","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1216\/JIE-2008-20-1-49","volume":"20","author":"Z Chen","year":"2008","unstructured":"Chen, Z., Wu, B., Xu, Y.: Fast collocation methods for high-dimensional weakly singular integral equaations. J. Integral Equ. Appl. 20, 49\u201392 (2008)","journal-title":"J. Integral Equ. Appl."},{"key":"9717_CR12","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1137\/S0036142996297217","volume":"35","author":"Z Chen","year":"1998","unstructured":"Chen, Z., Xu, Y.: The Petrov-Galerkin and interated Petrov-Galerkin methods for second kind integral equations. SIAM J. Numer. Anal. 35, 406\u2013434 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"9717_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1216\/jiea\/1181074260","volume":"11","author":"Z Chen","year":"1999","unstructured":"Chen, Z., Xu, Y., Zhao, J.: The discrete Petrov-Galerkin method for weakly singular integral equations. J. Integral Equ. Appl. 11, 1\u201335 (1999)","journal-title":"J. Integral Equ. Appl."},{"key":"9717_CR14","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/BF02571732","volume":"215","author":"W Dahmen","year":"1994","unstructured":"Dahmen, W., Proessdorf, S., Schneider, R.: Wavelet approximation methods for pseudodifferential equations I: stability and convergence. Math. Z. 215, 583\u2013620 (1994)","journal-title":"Math. Z."},{"key":"9717_CR15","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/BF02072014","volume":"1","author":"W Dahmen","year":"1993","unstructured":"Dahmen, W., Proessdorf, S., Schneider, R.: Wavelet approximation methods for psuedodifferential equations II: matrix compression and fast solutions. Adv. Comput. Math. 1, 259\u2013335 (1993)","journal-title":"Adv. Comput. Math."},{"key":"9717_CR16","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0021-9045(85)90073-5","volume":"44","author":"IG Graham","year":"1985","unstructured":"Graham, I.G.: Estimates for the modulus of smoothness. J. Appl. Theory 44, 95\u2013112 (1985)","journal-title":"J. Appl. Theory"},{"key":"9717_CR17","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1093\/imanum\/5.3.355","volume":"5","author":"IG Graham","year":"1985","unstructured":"Graham, I.G., Joe, S., Sloan, I.H.: Iterated Galerkin versus iterated collocation for integral equations of second kind. IMA J. Numer. Anal. 5, 355\u2013369 (1985)","journal-title":"IMA J. Numer. Anal."},{"key":"9717_CR18","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1216\/jiea\/1181075366","volume":"18","author":"M Huang","year":"2006","unstructured":"Huang, M., Xu, Y.: Superconvergence of the iterated hybrid collocation method for weakly singular Volterra integral equations. J. Integral Equ. Appl. 18, 83\u2013116 (2006)","journal-title":"J. Integral Equ. Appl."},{"key":"9717_CR19","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/S0377-0427(97)00040-X","volume":"80","author":"H Kaneko","year":"1997","unstructured":"Kaneko, H.: Superconvergence of the iterated collocation method for hammerstein equations. J. Comput. Appl. Math. 80, 335\u2013349 (1997)","journal-title":"J. Comput. Appl. Math."},{"key":"9717_CR20","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1080\/00036810108840996","volume":"80","author":"H Kaneko","year":"2001","unstructured":"Kaneko, H., Padilla, P., Xu, Y.: Superconvergence of the iterated degenerate kernel method. Appl. Anal. 80, 331\u2013351 (2001)","journal-title":"Appl. Anal."},{"key":"9717_CR21","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1090\/S0025-5718-1994-1218345-X","volume":"62","author":"H Kaneko","year":"1994","unstructured":"Kaneko, H., Xu, Y.: Gauss-type quadratures for weakly singular integrals and their application to fredholm integral equations of the second kind. Math. Comput. 62, 739\u2013753 (1994)","journal-title":"Math. Comput."},{"key":"9717_CR22","doi-asserted-by":"crossref","unstructured":"Kress, R.: Linear Integral Equations. Springer, Berlin (1989)","DOI":"10.1007\/978-3-642-97146-4"},{"key":"9717_CR23","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1137\/0727090","volume":"27","author":"Q Lin","year":"1990","unstructured":"Lin, Q., Sloan, I.H., Xie, R.: Extrapolation of the iterated collocation method for integral equations of the second kind. SIAM J. Numer. Anal. 27, 1535\u20131541 (1990)","journal-title":"SIAM J. Numer. Anal."},{"key":"9717_CR24","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1006\/acha.1994.1024","volume":"1","author":"CA Micchelli","year":"1994","unstructured":"Micchelli, C.A., Xu, Y.: Using the matrix refinement equation for the construction of wavelets on invarient sets. Comput. Harmonic Anal. 1, 391\u2013401 (1994)","journal-title":"Comput. Harmonic Anal."},{"key":"9717_CR25","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/S0377-0427(97)00160-X","volume":"86","author":"CA Micchelli","year":"1997","unstructured":"Micchelli, C.A., Xu, Y., Zhao, Y.: Wavelet Galerkin methods for second-kind integral equations. J. Comput. Appl. Math. 86, 251\u2013270 (1997)","journal-title":"J. Comput. Appl. Math."},{"key":"9717_CR26","volume-title":"Spline Functions: Basic Theory","author":"LL Schumer","year":"1981","unstructured":"Schumer, L.L.: Spline Functions: Basic Theory. Wiley, New York (1981)"},{"key":"9717_CR27","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/978-1-4899-2593-0_2","volume-title":"Numerical Solution of Integral Equations","author":"IH Sloan","year":"1990","unstructured":"Sloan, I.H.: Superconvergence. In: Golberg, M. (ed.) Numerical Solution of Integral Equations, pp. 35\u201370. Plenum, New York (1990)"},{"key":"9717_CR28","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s002110050226","volume":"74","author":"T Petersdorff von","year":"1996","unstructured":"von Petersdorff, T., Schwab, C.: Wavelet approximation for first kind boundary integral equations on polygons. Numer. Math. 74, 479\u2013516 (1996)","journal-title":"Numer. Math."},{"key":"9717_CR29","doi-asserted-by":"crossref","first-page":"2212","DOI":"10.1137\/S0036142994272957","volume":"34","author":"T Petersdorff von","year":"1997","unstructured":"von Petersdorff, T., Schwab, C., Schneider, R.: Multiwavelets for second kind integral equations. SIAM J. Numer. Anal. 34, 2212\u20132227 (1997)","journal-title":"SIAM J. Numer. Anal."},{"key":"9717_CR30","doi-asserted-by":"crossref","unstructured":"Vainikko, G.: Multidimensional Weakly Integral Equations. Springer-Verlag, New York (1993)","DOI":"10.1007\/BFb0088979"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9717-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-013-9717-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9717-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T04:45:43Z","timestamp":1559450743000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-013-9717-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,25]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["9717"],"URL":"https:\/\/doi.org\/10.1007\/s10915-013-9717-9","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,25]]}}}