{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:03Z","timestamp":1740123543100,"version":"3.37.3"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,10,13]],"date-time":"2017-10-13T00:00:00Z","timestamp":1507852800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Science and Technology Major Project","award":["J-GFZX020101010.4"],"award-info":[{"award-number":["J-GFZX020101010.4"]}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2017MA016"],"award-info":[{"award-number":["ZR2017MA016"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["41306002"],"award-info":[{"award-number":["41306002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["201562012"],"award-info":[{"award-number":["201562012"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the startup funding of Ocean University of China","award":["201712011"],"award-info":[{"award-number":["201712011"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,5]]},"DOI":"10.1007\/s10915-017-0572-y","type":"journal-article","created":{"date-parts":[[2017,10,13]],"date-time":"2017-10-13T21:23:11Z","timestamp":1507929791000},"page":"1016-1039","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fast Iterative Adaptive Multi-quadric Radial Basis Function Method for Edges Detection of Piecewise Functions\u2014I: Uniform Mesh"],"prefix":"10.1007","volume":"75","author":[{"given":"Wai Sun","family":"Don","sequence":"first","affiliation":[]},{"given":"Bao-Shan","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Zhen","family":"Gao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,10,13]]},"reference":[{"key":"572_CR1","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1007\/s10915-015-0088-2","volume":"67","author":"R Archibald","year":"2016","unstructured":"Archibald, R., Gelb, A., Platte, R.B.: Image reconstruction from undersampled Fourier data using the polynomial annihilation transform. J. Sci. Comput. 67, 432\u2013452 (2016)","journal-title":"J. Sci. Comput."},{"key":"572_CR2","doi-asserted-by":"crossref","first-page":"3101","DOI":"10.1016\/j.jcp.2007.11.038","volume":"227","author":"R Borges","year":"2008","unstructured":"Borges, R., Carmona, M., Costa, B., Don, W.S.: An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws. J. Comput. Phys. 227, 3101\u20133211 (2008)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"572_CR3","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1023\/A:1014584220418","volume":"16","author":"M Bozzini","year":"2002","unstructured":"Bozzini, M., Lenarduzzi, L., Schaback, R.: Adaptive interpolation by scaled multiquadrics. Adv. Comput. Math. 16(4), 375\u2013387 (2002)","journal-title":"Adv. Comput. Math."},{"key":"572_CR4","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1017\/S0013091500018411","volume":"36","author":"MD Buhmann","year":"1993","unstructured":"Buhmann, M.D., Dyn, N.: Spectral convergence of multiquadric interpolation. Proc. Edinb. Math. Soc. 36, 319\u2013333 (1993)","journal-title":"Proc. Edinb. Math. Soc."},{"key":"572_CR5","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511543241","volume-title":"Radial Basis Functions: Theory and Implementations","author":"MD Buhmann","year":"2003","unstructured":"Buhmann, M.D.: Radial Basis Functions: Theory and Implementations. Cambridge University Press, Cambridge (2003)"},{"key":"572_CR6","doi-asserted-by":"crossref","unstructured":"Carr, J., Beatson, R., Cherrie, J., Mitchell, T., Fright, W., McCallum, B., Evans, T.: Reconstruction and representation of 3D objects with radial basis functions. In: SIGGRAPH, pp. 67\u201376 (2001)","DOI":"10.1145\/383259.383266"},{"key":"572_CR7","doi-asserted-by":"crossref","first-page":"1766","DOI":"10.1016\/j.jcp.2010.11.028","volume":"230","author":"M Castro","year":"2011","unstructured":"Castro, M., Costa, B., Don, W.S.: High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws. J. Comput. Phys. 230, 1766\u20131792 (2011)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"572_CR8","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1137\/040617200","volume":"29","author":"S Chandrasekaran","year":"2007","unstructured":"Chandrasekaran, S., Gu, M., Sun, X., Xia, J., Zhu, J.: A superfast algorithm for Toeplitz systems of linear equations. SIAM J. Matrix Anal. Appl. 29(4), 1247\u20131266 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"19","key":"572_CR9","doi-asserted-by":"crossref","first-page":"7473","DOI":"10.1016\/j.jcp.2009.07.005","volume":"228","author":"J Chao","year":"2009","unstructured":"Chao, J., Haselbacher, A., Balachandar, S.: A massively parallel multi-block hybrid compact-WENO scheme for compressible flows. J. Comput. Phys. 228(19), 7473\u20137491 (2009)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"572_CR10","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.cam.2006.01.039","volume":"204","author":"B Costa","year":"2007","unstructured":"Costa, B., Don, W.S.: High order hybrid central-WENO finite difference scheme for conservation laws. J. Comput. Appl. Math. 204(2), 209\u2013218 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"572_CR11","doi-asserted-by":"crossref","first-page":"970","DOI":"10.1016\/j.jcp.2006.11.002","volume":"224","author":"B Costa","year":"2007","unstructured":"Costa, B., Don, W.S.: Multi-domain hybrid spectral-WENO methods for hyperbolic conservation laws. J. Comput. Phys. 224, 970\u2013991 (2007)","journal-title":"J. Comput. Phys."},{"key":"572_CR12","first-page":"411","volume":"52","author":"B Cockburn","year":"1989","unstructured":"Cockburn, B., Shu, C.-W.: TVB Runge\u2013Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math. Comput. 52, 411\u2013435 (1989)","journal-title":"Math. Comput."},{"issue":"2","key":"572_CR13","doi-asserted-by":"crossref","first-page":"A559","DOI":"10.1137\/16M1068013","volume":"39","author":"D Denker","year":"2017","unstructured":"Denker, D., Gelb, A.: Edge detection of piecewise smooth functions from undersampled Fourier data using variance signatures. SIAM J. Sci. Comput. 39(2), A559\u2013A592 (2017)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"572_CR14","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1137\/15M1021520","volume":"38","author":"WS Don","year":"2016","unstructured":"Don, W.S., Gao, Z., Li, P., Wen, X.: Hybrid compact-WENO finite difference scheme with conjugate Fourier shock detection algorithm for hyperbolic conservation laws. SIAM J. Sci. Comput. 38(2), 691\u2013711 (2016)","journal-title":"SIAM J. Sci. Comput."},{"key":"572_CR15","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1016\/j.camwa.2006.06.005","volume":"53","author":"TA Driscoll","year":"2007","unstructured":"Driscoll, T.A., Heryudono, A.R.H.: Adaptive residual subsampling methods for radial basis function interpolation and collocation problems. Comput. Math. Appl. 53, 927\u2013939 (2007)","journal-title":"Comput. Math. Appl."},{"key":"572_CR16","first-page":"73","volume":"93","author":"C Franke","year":"1988","unstructured":"Franke, C., Schaback, R.: Solving partial differential equations by collocation using radial basis functions. Appl. Math. Comput. 93, 73\u201383 (1988)","journal-title":"Appl. Math. Comput."},{"key":"572_CR17","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1137\/080725891","volume":"2","author":"T Goldsten","year":"2009","unstructured":"Goldsten, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2, 323\u2013343 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"572_CR18","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s10915-012-9635-2","volume":"55","author":"Z Gao","year":"2012","unstructured":"Gao, Z., Don, W.S.: Mapped hybrid central-WENO finite difference scheme for detonation waves simulations. J. Sci. Comput. 55, 351\u2013371 (2012)","journal-title":"J. Sci. Comput."},{"key":"572_CR19","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1090\/S0025-5718-1995-1312096-X","volume":"64","author":"I Gohberg","year":"1995","unstructured":"Gohberg, I., Kailath, T., Olshevsky, V.: Fast Gaussian elimination with partial pivoting for matrices with displacement structure. Math. Comput. 64, 1557\u20131576 (1995)","journal-title":"Math. Comput."},{"key":"572_CR20","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0021-9991(83)90136-5","volume":"49","author":"A Harten","year":"1983","unstructured":"Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357\u2013393 (1983)","journal-title":"J. Comput. Phys."},{"key":"572_CR21","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1137\/S0895479895291273","volume":"19","author":"M Gu","year":"1998","unstructured":"Gu, M.: Stable and efficient algorithms for structured systems of linear equations. SIAM J. Matrix Anal. Appl. 19, 279\u2013306 (1998)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"572_CR22","first-page":"63","volume-title":"Linear Algebra for Signal Processing (The IMA Volumes in Mathematics and Its Applications)","author":"G Heinig","year":"1995","unstructured":"Heinig, G.: Inversion of generalized Cauchy matrices and other classes of structured matrices. In: Bojanczyk, A., Cybenko, G. (eds.) Linear Algebra for Signal Processing (The IMA Volumes in Mathematics and Its Applications), vol. 69, pp. 63\u201381. Springer, New York (1995)"},{"key":"572_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.laa.2010.12.001","volume":"435","author":"G Heinig","year":"2011","unstructured":"Heinig, G., Rost, K.: Fast algorithms for Toeplitz and Hankel matrices. Linear Algebra Appl. 435, 1\u201359 (2011)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"572_CR24","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1023\/A:1022253303343","volume":"32","author":"YC Hon","year":"2003","unstructured":"Hon, Y.C., Schaback, R., Zhou, X.: An adaptive greedy algorithm for solving large RBF collocation problems. Numer. Algorithms 32(1), 13\u201325 (2003)","journal-title":"Numer. Algorithms"},{"key":"572_CR25","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.apnum.2006.02.006","volume":"57","author":"J-H Jung","year":"2007","unstructured":"Jung, J.-H.: A note on the Gibbs phenomenon with multiquadric radial basis functions. Appl. Numer. Math. 57, 213\u2013229 (2007)","journal-title":"Appl. Numer. Math."},{"key":"572_CR26","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1016\/j.apnum.2008.09.002","volume":"59","author":"J-H Jung","year":"2009","unstructured":"Jung, J.-H., Durante, V.: An iterative multiquadric radial basis function method for the detection of local jump discontinuities. Appl. Numer. Math. 59, 1449\u20131446 (2009)","journal-title":"Appl. Numer. Math."},{"key":"572_CR27","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.apnum.2010.08.006","volume":"61","author":"J-H Jung","year":"2011","unstructured":"Jung, J.-H., Gottlieb, S., Kim, S.O.: Iterative adaptive RBF methods for detection of edges in two-dimensional functions. Appl. Numer. Math. 61, 77\u201391 (2011)","journal-title":"Appl. Numer. Math."},{"key":"572_CR28","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0898-1221(90)90271-K","volume":"19","author":"EJ Kansa","year":"1990","unstructured":"Kansa, E.J.: Muliquadrics\u2014a scattered data approximation scheme with applications to computational fluid dynamics: II. Solutions to parabolic, hyperbolic, and elliptic partial differential equations. Comput. Math. Appl. 19, 147\u2013161 (1990)","journal-title":"Comput. Math. Appl."},{"key":"572_CR29","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0898-1221(00)00071-7","volume":"39","author":"EJ Kansa","year":"2000","unstructured":"Kansa, E.J., Hon, Y.C.: Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Comput. Math. Appl. 39, 123\u2013137 (2000)","journal-title":"Comput. Math. Appl."},{"key":"572_CR30","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/j.enganabound.2006.12.001","volume":"31","author":"EJ Kansa","year":"2007","unstructured":"Kansa, E.J.: Exact explicit time integration of hyperbolic partial differential equations with mesh free radial basis functions. Eng. Anal. Bound. Elem. 31, 577\u2013585 (2007)","journal-title":"Eng. Anal. Bound. Elem."},{"key":"572_CR31","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.apnum.2003.11.002","volume":"48","author":"L Krivodonova","year":"2004","unstructured":"Krivodonova, L., Xin, J., Remacle, J.-F., Chevaugeon, N., Flaherty, J.: Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws. Appl. Numer. Math. 48, 323\u2013338 (2004)","journal-title":"Appl. Numer. Math."},{"key":"572_CR32","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1016\/S0898-1221(03)90151-9","volume":"46","author":"E Larsson","year":"2003","unstructured":"Larsson, E., Fornberg, B.: A numerical study of some radial basis function based solution methods for elliptic PDEs. Comput. Math. Appl. 46, 891\u2013902 (2003)","journal-title":"Comput. Math. Appl."},{"key":"572_CR33","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0898-1221(92)90175-H","volume":"24","author":"WR Madych","year":"1992","unstructured":"Madych, W.R.: Miscellaneous error bounds for multiquadric and related interpolators. Comput. Math. Appl. 24, 121\u2013138 (1992)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"572_CR34","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/0021-9045(92)90058-V","volume":"70","author":"WR Madych","year":"1992","unstructured":"Madych, W.R., Nelson, S.A.: Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation. J. Approx. Theory 70(1), 94\u2013114 (1992)","journal-title":"J. Approx. Theory"},{"issue":"1","key":"572_CR35","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1006\/jcph.2002.7021","volume":"178","author":"S Pirozzoli","year":"2002","unstructured":"Pirozzoli, S.: Conservative hybrid compact-WENO schemes for shock\u2013turbulence interaction. J. Comput. Phys. 178(1), 81\u2013117 (2002)","journal-title":"J. Comput. Phys."},{"key":"572_CR36","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.jcp.2003.07.006","volume":"192","author":"YX Ren","year":"2003","unstructured":"Ren, Y.X., Liu, M., Zhang, H.: A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws. J. Comput. Phys. 192, 365\u2013386 (2003)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"572_CR37","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1023\/A:1019105612985","volume":"24","author":"R Schaback","year":"2000","unstructured":"Schaback, R., Wendland, H.: Adaptive greedy techniques for approximate solution of large RBF systems. Numer. Algorithms 24(3), 239\u2013254 (2000)","journal-title":"Numer. Algorithms"},{"issue":"4","key":"572_CR38","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1002\/fld.1286","volume":"53","author":"YQ Shen","year":"2007","unstructured":"Shen, Y.Q., Yang, G.W.: Hybrid finite compact-WENO schemes for shock calculation. Int. J. Numer. Methods Fluids 53(4), 531\u2013560 (2007)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"572_CR39","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1137\/0112045","volume":"12","author":"W Trench","year":"1964","unstructured":"Trench, W.: An algorithm for the inversion of finite Toeplitz matrices. SIAM J. Appl. Math. 12, 515\u2013522 (1964)","journal-title":"SIAM J. Appl. Math."},{"key":"572_CR40","unstructured":"http:\/\/sipi.usc.edu\/database\/database.php?volume=misc"},{"issue":"1","key":"572_CR41","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1006\/jcph.1998.6060","volume":"146","author":"O Vasilyev","year":"1998","unstructured":"Vasilyev, O., Lund, T., Moin, P.: A general class of commutative filters for LES in complex geometries. J. Comput. Phys. 146(1), 82\u2013104 (1998)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"572_CR42","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1137\/120895755","volume":"35","author":"Y Xi","year":"2014","unstructured":"Xi, Y., Xia, J., Cauley, S., Balakrishnan, V.: Superfast and stable structured solvers for Toeplitz least squares via randomized sampling. SIAM J. Matrix Anal. Appl. 35(1), 44\u201372 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"572_CR43","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1137\/110831982","volume":"33","author":"J Xia","year":"2012","unstructured":"Xia, J., Xi, Y., Gu, M.: A superfast structured solver for Toeplitz linear systems via randomized sampling. SIAM J. Matrix Anal. Appl. 33(3), 837\u2013858 (2012)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"572_CR44","volume-title":"Regularized Radial Basis Function Networks: Theory and Applications","author":"PV Yee","year":"2001","unstructured":"Yee, P.V., Haykin, S.: Regularized Radial Basis Function Networks: Theory and Applications. Wiley, New York (2001)"},{"key":"572_CR45","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1137\/S0036141000373811","volume":"33","author":"J Yoon","year":"2001","unstructured":"Yoon, J.: Spectral approximation orders of radial basis function interpolation on the Sobolev space. SIAM J. Math. Anal. 33, 946\u2013958 (2001)","journal-title":"SIAM J. Math. Anal."},{"key":"572_CR46","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0168-9274(02)00107-1","volume":"44","author":"X Zhou","year":"2003","unstructured":"Zhou, X., Hon, Y.C., Li, J.: Overlapping domain decomposition method by radial basis functions. Appl. Numer. Math. 44, 241\u2013255 (2003)","journal-title":"Appl. Numer. Math."},{"key":"572_CR47","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.apnum.2016.10.001","volume":"112","author":"QQ Zhu","year":"2017","unstructured":"Zhu, Q.Q., Gao, Z., Don, W.S., Lv, X.Q.: Well-balanced hybrid compact-WENO schemes for shallow water equations. Appl. Numer. Math. 112, 65\u201378 (2017)","journal-title":"Appl. Numer. Math."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0572-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0572-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0572-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T10:18:44Z","timestamp":1589797124000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0572-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,13]]},"references-count":47,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,5]]}},"alternative-id":["572"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0572-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2017,10,13]]}}}