{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T04:04:49Z","timestamp":1751947489317,"version":"3.41.2"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1-4","license":[{"start":{"date-parts":[[2001,12,1]],"date-time":"2001-12-01T00:00:00Z","timestamp":1007164800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2001,12,1]],"date-time":"2001-12-01T00:00:00Z","timestamp":1007164800000},"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":["Numerical Algorithms"],"published-print":{"date-parts":[[2001,12]]},"DOI":"10.1023\/a:1014030412645","type":"journal-article","created":{"date-parts":[[2003,3,21]],"date-time":"2003-03-21T00:56:49Z","timestamp":1048208209000},"page":"101-116","source":"Crossref","is-referenced-by-count":5,"title":["Approximating the Approximant: A Numerical Code for Polynomial Compression of Discrete Integral Operators"],"prefix":"10.1007","volume":"28","author":[{"given":"Stefano","family":"De Marchi","sequence":"first","affiliation":[]},{"given":"Marco","family":"Vianello","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"391464_CR1","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1137\/0914010","volume":"14","author":"B. Alpert","year":"1993","unstructured":"B. Alpert, G. Beylkin, R. Coifman and V. Rokhlin, Wavelet-like bases for the fast solution of secondkind integral equations, SIAM J. Sci. Comput. 14 (1993) 159\u2013184.","journal-title":"SIAM J. Sci. Comput."},{"key":"391464_CR2","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1216\/jiea\/1181075664","volume":"4","author":"K.E. Atkinson","year":"1992","unstructured":"K.E. Atkinson, A survey of numerical methods for solving nonlinear integral equations, J. Integral Equations Appl. 4 (1992) 15\u201346.","journal-title":"J. Integral Equations Appl."},{"key":"391464_CR3","series-title":"Cambridge Monographs on Applied and Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511626340","volume-title":"The Numerical Solution of Integral Equations of the Second Kind","author":"K.E. Atkinson","year":"1997","unstructured":"K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge Monographs on Applied and Computational Mathematics, Vol. 4 (Cambridge University Press, Cambridge, 1997)."},{"key":"391464_CR4","first-page":"189","volume":"6","author":"L. Bos","year":"2000","unstructured":"L. Bos and S. De Marchi, Fekete points for bivariate polynomials restricted to y = x\nm, East J. Approx. 6 (2000) 189\u2013200.","journal-title":"East J. Approx."},{"key":"391464_CR5","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.1090\/S0025-5718-00-01262-X","volume":"70","author":"L. Bos","year":"2001","unstructured":"L. Bos, M.A. Taylor and B.A. Wingate, Tensor product Gauss-Lobatto points are Fekete points for the cube, Math. Comp. 70 (2001) 1543\u20131547.","journal-title":"Math. Comp."},{"key":"391464_CR6","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1137\/S106482759528555X","volume":"19","author":"A. Brandt","year":"1998","unstructured":"A. Brandt and C.H. Venner, Multilevel evaluation of integral transforms with asymptotically smooth kernels, SIAM J. Sci. Comput. 19 (1998) 468\u2013492.","journal-title":"SIAM J. Sci. Comput."},{"key":"391464_CR7","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1017\/S0962492900002713","volume":"6","author":"W. Dahmen","year":"1997","unstructured":"W. Dahmen, Wavelet and multiscale methods for operator equations, Acta Numer. 6 (1997) 55\u2013228.","journal-title":"Acta Numer."},{"key":"391464_CR8","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1002\/(SICI)1099-1506(199707\/08)4:4<273::AID-NLA97>3.0.CO;2-T","volume":"4","author":"S.A. Goreinov","year":"1997","unstructured":"S.A. Goreinov, E.E. Tyrtyshnikov and A.Yu. Yeremin, Matrix-free iterative solution strategies for large dense linear systems, Numer. Linear Algebra Appl. 4 (1997) 273\u2013294.","journal-title":"Numer. Linear Algebra Appl."},{"key":"391464_CR9","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1126\/science.265.5174.909","volume":"265","author":"L. Greengard","year":"1994","unstructured":"L. Greengard, Fast algorithms for classical physics, Science 265 (1994) 909\u2013914.","journal-title":"Science"},{"key":"391464_CR10","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/0021-9991(87)90140-9","volume":"73","author":"L. Greengard","year":"1987","unstructured":"L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Comput. Phys. 73 (1987) 325\u2013348.","journal-title":"J. Comput. Phys."},{"key":"391464_CR11","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1017\/S0962492900002725","volume":"6","author":"L. Greengard","year":"1997","unstructured":"L. Greengard and V. Rokhlin, A new version of the fast multipole method for the Laplace equation in three dimensions, Acta Numer. 6 (1997) 229\u2013269.","journal-title":"Acta Numer."},{"key":"391464_CR12","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1137\/0912004","volume":"12","author":"L. Greengard","year":"1991","unstructured":"L. Greengard and J. Strain, The fast Gauss transform, SIAM J. Sci. Stat. Comput. 12 (1991) 79\u201394.","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"391464_CR13","first-page":"575","volume":"III","author":"L. Greengard","year":"1998","unstructured":"L. Greengard and X. Sun, A new version of the fast Gauss transform, in: Proceedings of the International Congress of Mathematicians, Berlin, 1998, Vol. III, Doc. Math. 1998, Extra Vol. III, pp. 575\u2013584.","journal-title":"Proceedings of the International Congress of Mathematicians, Berlin"},{"key":"391464_CR14","series-title":"International Series of Numerical Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-9215-5","volume-title":"Integral Equations: Theory and Numerical Treatment","author":"W. Hackbusch","year":"1995","unstructured":"W. Hackbusch, Integral Equations: Theory and Numerical Treatment, International Series of Numerical Mathematics, Vol. 120 (Birkh\u00e4user, Basel, 1995)."},{"key":"391464_CR15","doi-asserted-by":"crossref","unstructured":"W. Hackbusch, A sparse matrix arithmetic based on 115\u20131-matrices. I. Introduction to 115\u20132-matrices, Computing 62 (1999) 89\u2013108.","DOI":"10.1007\/s006070050015"},{"key":"391464_CR16","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/PL00021408","volume":"64","author":"W. Hackbusch","year":"2000","unstructured":"W. Hackbusch and B.N. Khoromskij, A sparse 115\u20133-matrix arithmetic. II. Application to multidimensional problems, Computing 64 (2000) 21\u201347.","journal-title":"Computing"},{"key":"391464_CR17","doi-asserted-by":"crossref","unstructured":"W. Hackbusch and B.N. Khoromskij, Towards 115\u20134-matrix approximation of the linear complexity, in: Operator Theory: Advances and Applications, Vol. 121 (Birkh\u00e4user, 2001) pp. 194\u2013220.","DOI":"10.1007\/978-3-0348-8276-7_13"},{"key":"391464_CR18","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/BF01396324","volume":"54","author":"W. Hackbusch","year":"1989","unstructured":"W. Hackbusch and Z. Nowak, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math. 54 (1989) 463\u2013491.","journal-title":"Numer. Math."},{"key":"391464_CR19","doi-asserted-by":"crossref","first-page":"1138","DOI":"10.1137\/0725065","volume":"25","author":"C.T. Kelley","year":"1988","unstructured":"C.T. Kelley and J.I. Northrup, A pointwise quasi-Newton method for integral equations, SIAM J. Numer. Anal. 25 (1988) 1138\u20131155.","journal-title":"SIAM J. Numer. Anal."},{"key":"391464_CR20","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1006\/jcph.1995.1217","volume":"122","author":"S.R. Lustig","year":"1995","unstructured":"S.R. Lustig, S. Rastogi and N. Wagner, Telescoping fast multipole methods using Chebyshev economization, J. Comput. Phys. 122 (1995) 317\u2013322.","journal-title":"J. Comput. Phys."},{"key":"391464_CR21","unstructured":"G. Monegato and L. Scuderi, Weighted Sobolev-type spaces and numerical methods for 1D integral equations, invited talk in: 4th International Conference on Functional Analysis and Approximation Theory, Acquafredda di Maratea, PZ, Italy (September 2000)."},{"key":"391464_CR22","doi-asserted-by":"crossref","DOI":"10.1002\/9781118033210","volume-title":"The Mollification Method and the Numerical Solution of Ill-Posed Problems","author":"D.A. Murio","year":"1993","unstructured":"D.A. Murio, The Mollification Method and the Numerical Solution of Ill-Posed Problems (Wiley, New York, 1993)."},{"key":"391464_CR23","first-page":"113","volume":"121","author":"R. Piessens","year":"2000","unstructured":"R. Piessens, Computing integral transforms and solving integral equations using Chebyshev polynomial approximations, in: Numerical Analysis in the 20th Century, Vol. I, Approximation Theory, J. Comput. Appl. Math. 121 (2000) 113\u2013124.","journal-title":"Numerical Analysis in the 20th Century, Vol. I, Approximation Theory, J. Comput. Appl. Math."},{"key":"391464_CR24","volume-title":"An Introduction to the Approximation of Functions","author":"T.J. Rivlin","year":"1981","unstructured":"T.J. Rivlin, An Introduction to the Approximation of Functions (Dover, New York, 1981)."},{"key":"391464_CR25","volume-title":"Chebyshev Polynomials","author":"T.J. Rivlin","year":"1990","unstructured":"T.J. Rivlin, Chebyshev Polynomials (Wiley, New York, 1990)."},{"key":"391464_CR26","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/0021-9991(85)90002-6","volume":"60","author":"V. Rokhlin","year":"1985","unstructured":"V. Rokhlin, Rapid solution of integral equations of classical potential theory, J. Comput. Phys. 60 (1985) 187\u2013207.","journal-title":"J. Comput. Phys."},{"key":"391464_CR27","unstructured":"A. Sommariva, A fast Nystr\u00f6m-Broyden solver by Chebyshev compression, in preparation."},{"key":"391464_CR28","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1216\/jiea\/1020282136","volume":"12","author":"A. Sommariva","year":"2000","unstructured":"A. Sommariva and M. Vianello, Computing positive fixed-points of decreasing Hammerstein operators by relaxed iterations, J. Integral Equations Appl. 12 (2000) 95\u2013112.","journal-title":"J. Integral Equations Appl."},{"key":"391464_CR29","doi-asserted-by":"crossref","first-page":"1707","DOI":"10.1137\/S0036142998337247","volume":"38","author":"M.A. Taylor","year":"2000","unstructured":"M.A. Taylor, B.A. Wingate and R.E. Vincent, An algorithm for computing Fekete points in the triangle, SIAM J. Numer. Anal. 38 (2000) 1707\u20131720.","journal-title":"SIAM J. Numer. Anal."},{"key":"391464_CR30","first-page":"327","volume":"8","author":"M. Vianello","year":"2000","unstructured":"M. Vianello, Chebyshev-like compression of linear and nonlinear discretized integral operators, Neural, Parallel and Sci. Comput. 8 (2000) 327\u2013353.","journal-title":"Neural, Parallel and Sci. Comput."},{"key":"391464_CR31","doi-asserted-by":"crossref","first-page":"2212","DOI":"10.1137\/S0036142994272957","volume":"34","author":"T. von Petersdorff","year":"1997","unstructured":"T. von Petersdorff, C. Schwab and R. Schneider, Multiwavelets for second-kind integral equations, SIAM J. Numer. Anal. 34 (1997) 2212\u20132227.","journal-title":"SIAM J. Numer. Anal."},{"key":"391464_CR32","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/S0898-1221(99)00116-9","volume":"37","author":"S. Zhan","year":"1999","unstructured":"S. Zhan and D.A. Murio, Surface fitting and numerical gradient computations by discrete mollification, Comput. Math. Appl. 37 (1999) 85\u2013102.","journal-title":"Comput. Math. Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014030412645.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1014030412645\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014030412645.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T07:14:49Z","timestamp":1751872489000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1014030412645"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,12]]},"references-count":32,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2001,12]]}},"alternative-id":["391464"],"URL":"https:\/\/doi.org\/10.1023\/a:1014030412645","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2001,12]]}}}