{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T09:13:20Z","timestamp":1775121200145,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T00:00:00Z","timestamp":1555977600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK 2088"],"award-info":[{"award-number":["GRK 2088"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s10444-019-09692-y","type":"journal-article","created":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T07:02:44Z","timestamp":1556002964000},"page":"1657-1687","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Optimal approximation with exponential sums by a maximum likelihood modification of Prony\u2019s method"],"prefix":"10.1007","volume":"45","author":[{"given":"Ran","family":"Zhang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3232-0573","authenticated-orcid":false,"given":"Gerlind","family":"Plonka","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,4,23]]},"reference":[{"issue":"1","key":"9692_CR1","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1070\/SM1971v015n01ABEH001531","volume":"15","author":"VM Adamjan","year":"1971","unstructured":"Adamjan, V.M., Arov, D.Z., Krein, M.G.: Analytic properties of the Schmidt pairs of a Hankel operator and the generalized Schur-Takagi problem. Math. USSR-Sbornik 15(1), 31\u201373 (1971)","journal-title":"Math. USSR-Sbornik"},{"key":"9692_CR2","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/j.jat.2010.09.005","volume":"163","author":"F Andersson","year":"2011","unstructured":"Andersson, F., Carlsson, M., de Hoop, M.V.: Sparse approximation of functions using sums of exponentials and AAK theory. J. Approx. Theory 163, 213\u2013248 (2011)","journal-title":"J. Approx. Theory"},{"issue":"1","key":"9692_CR3","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.acha.2017.03.004","volume":"46","author":"F Andersson","year":"2019","unstructured":"Andersson, F., Carlsson, M.: Fixed-point algorithms for frequency estimation and structured low-rank approximation. Appl. Comput. Harmon. Anal. 46(1), 40\u201365 (2019)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"1","key":"9692_CR4","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/S0378-3758(01)00287-7","volume":"110","author":"ZD Bai","year":"2003","unstructured":"Bai, Z.D., Rao, C.R., Chow, M., Kundu, D.: An efficient algorithm for estimating the parameters of superimposed exponential signals. J. Statist. Plann. Inference 110(1), 23\u201334 (2003)","journal-title":"J. Statist. Plann. Inference"},{"key":"9692_CR5","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.acha.2005.01.003","volume":"19","author":"G Beylkin","year":"2005","unstructured":"Beylkin, G., Monz\u00f3n, L.: On approximation of functions by exponential sums. Appl. Comput. Harmon. Anal. 19, 17\u201348 (2005)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9692_CR6","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.acha.2009.08.011","volume":"28","author":"G Beylkin","year":"2010","unstructured":"Beylkin, G., Monz\u00f3n, L.: Approximation by exponential sums revisited. Appl. Comput. Harmon. Anal. 28, 131\u2013148 (2010)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"1","key":"9692_CR7","doi-asserted-by":"publisher","first-page":"117","DOI":"10.2478\/amcs-2013-0010","volume":"23","author":"J Bian","year":"2003","unstructured":"Bian, J., Peng, H., Xing, J., Liu, Z., Li, H.: An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise. Int. J. Appl. Math. Comput. Sci. 23(1), 117\u2013129 (2003)","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"9692_CR8","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10921-012-0138-8","volume":"31","author":"F Bo\u00dfmann","year":"2012","unstructured":"Bo\u00dfmann, F., Plonka, G., Peter, T., Nemitz, O., Schmitte, T.: Sparse deconvolution methods for ultrasonic NDT. J. Nondestruct. Eval. 31, 225\u2013244 (2012)","journal-title":"J. Nondestruct. Eval."},{"key":"9692_CR9","doi-asserted-by":"crossref","unstructured":"Braess, D., Hackbusch, W.: On the efficient computation of high-dimensional integrals and the approximation by exponential sums. In: DeVore, R.A., Kunoth, A. (eds.) Multiscale, Nonlinear and Adaptive Approximation. Springer, Berlin (2009)","DOI":"10.1007\/978-3-642-03413-8_3"},{"issue":"5","key":"9692_CR10","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1109\/TASSP.1986.1164949","volume":"34","author":"Y Bresler","year":"1986","unstructured":"Bresler, Y., Macovski, A.: Exact maximum likelihood parameter estimation of superimposed exponential signals in noise. IEEE Trans. Acoust., Speech, Signal Process. ASSP 34(5), 1081\u20131089 (1986)","journal-title":"IEEE Trans. Acoust., Speech, Signal Process. ASSP"},{"issue":"22","key":"9692_CR11","doi-asserted-by":"publisher","first-page":"6024","DOI":"10.1109\/TSP.2015.2461513","volume":"63","author":"Z Dogan","year":"2015","unstructured":"Dogan, Z., Gilliam, C., Blue, T., Van de Ville, D.: Reconstruction of finite rate of innovation signals with model-fitting approach. IEEE Trans. Signal Process. 63(22), 6024\u20136036 (2015)","journal-title":"IEEE Trans. Signal Process."},{"key":"9692_CR12","doi-asserted-by":"publisher","first-page":"1741","DOI":"10.1109\/TSP.2006.890907","volume":"55","author":"PL Dragotti","year":"2007","unstructured":"Dragotti, P.L., Vetterli, M., Blu, T.: Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets Strang\u2013Fix. IEEE Trans. Signal Process. 55, 1741\u20131757 (2007)","journal-title":"IEEE Trans. Signal Process."},{"issue":"4","key":"9692_CR13","doi-asserted-by":"publisher","first-page":"2088","DOI":"10.1109\/TPWRD.2006.881984","volume":"21","author":"EA Feilat","year":"2006","unstructured":"Feilat, E.A.: Prony analysis technique for estimation of the mean curve of lightning impulses. IEEE Trans. Power Del. 21(4), 2088\u20132090 (2006)","journal-title":"IEEE Trans. Power Del."},{"issue":"2","key":"9692_CR14","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1137\/0710036","volume":"10","author":"GH Golub","year":"1973","unstructured":"Golub, G.H., Pereyra, V.: The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal. 10(2), 413\u2013432 (1973)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9692_CR15","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1137\/110823985","volume":"5","author":"M Hanke","year":"2012","unstructured":"Hanke, M.: One shot inverse scattering via rational approximation. SIAM J. Imaging Sci. 5(1), 465\u2013482 (2012)","journal-title":"SIAM J. Imaging Sci."},{"issue":"12","key":"9692_CR16","doi-asserted-by":"publisher","first-page":"2186","DOI":"10.1109\/29.61547","volume":"38","author":"Y Hua","year":"1990","unstructured":"Hua, Y., Sarkar, T.K.: On the total least squares linear prediction method for frequency estimation. IEEE Trans. Acoust. Speech Signal Process., ASSP 38(12), 2186\u20132189 (1990)","journal-title":"IEEE Trans. Acoust. Speech Signal Process., ASSP"},{"issue":"3","key":"9692_CR17","doi-asserted-by":"publisher","first-page":"1180","DOI":"10.1137\/130931655","volume":"35","author":"M Ishteva","year":"2014","unstructured":"Ishteva, M., Usevich, K., Markovsky, I.: Factorization approach to structured low-rank approximation applications. SIAM J. Matrix Anal. Appl. 35(3), 1180\u20131204 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9692_CR18","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/10618600.1992.10474589","volume":"1","author":"MH Kahn","year":"1992","unstructured":"Kahn, M.H., Mackisack, M.S., Osborne, M.R., Smyth, G.K.: On the consistency of Prony\u2019s method and related algorithms. J. Comp. Graph. Statist. 1, 329\u2013349 (1992)","journal-title":"J. Comp. Graph. Statist."},{"issue":"3","key":"9692_CR19","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1109\/TASSP.1986.1164843","volume":"34","author":"R Kumaresan","year":"1986","unstructured":"Kumaresan, R., Scharf, L.L., Shaw, A.K.: An algorithm for pole-zero modeling and spectral analysis. IEEE Trans. Acoust. Speech Signal Process. ASSP 34(3), 637\u2013640 (1986)","journal-title":"IEEE Trans. Acoust. Speech Signal Process. ASSP"},{"issue":"1","key":"9692_CR20","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1109\/78.651203","volume":"46","author":"J Li","year":"1998","unstructured":"Li, J., Stoica, P., Liu, Z.-S.: Comparative study of IQML and mode direction-of-arrival estimators. IEEE Trans. Signal Process. 46(1), 149\u2013160 (1998)","journal-title":"IEEE Trans. Signal Process."},{"key":"9692_CR21","doi-asserted-by":"crossref","unstructured":"Markovsky, I.: Low-Rank Approximation: Algorithms, Implementation, Applications, 2nd edn. Springer (2018)","DOI":"10.1007\/978-3-319-89620-5"},{"key":"9692_CR22","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1016\/j.cam.2013.07.048","volume":"256","author":"I Markovsky","year":"2014","unstructured":"Markovsky, I., Usevich, K.: Software for weighted structured low-rank approximation. J. Comput. Appl. Math. 256, 278\u2013292 (2014)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"9692_CR23","first-page":"012013","volume":"659","author":"C Ortbandt","year":"2015","unstructured":"Ortbandt, C., Dzienis, C., Matussek, R., Schulte, H.: Parameter estimation in electrical power systems using Prony\u2019s method. J. Phys. 659(1), 012013 (2015)","journal-title":"J. Phys."},{"key":"9692_CR24","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1137\/0712044","volume":"12","author":"MR Osborne","year":"1975","unstructured":"Osborne, M.R.: Some Special nonlinear least square problems. SIAM J. Numer. Anal. 12, 571\u2013592 (1975)","journal-title":"SIAM J. Numer. Anal."},{"key":"9692_CR25","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1137\/0912020","volume":"12","author":"MR Osborne","year":"1991","unstructured":"Osborne, M.R., Smyth, G.K.: A modified Prony algorithm for fitting functions defined by difference equations. SIAM J. Sci. Stat. Comput. 12, 362\u2013382 (1991)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"1","key":"9692_CR26","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1137\/0916008","volume":"16","author":"MR Osborne","year":"1995","unstructured":"Osborne, M.R., Smyth, G.K.: A modified Prony algorithm for exponential function fitting. SIAM J. Sci. Comput. 16(1), 119\u2013138 (1995)","journal-title":"SIAM J. Sci. Comput."},{"key":"9692_CR27","doi-asserted-by":"publisher","first-page":"025001","DOI":"10.1088\/0266-5611\/29\/2\/025001","volume":"29","author":"T Peter","year":"2013","unstructured":"Peter, T., Plonka, G.: A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators. Inverse Probl. 29, 025001 (2013)","journal-title":"Inverse Probl."},{"key":"9692_CR28","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1111\/j.1365-246X.1973.tb03424.x","volume":"33","author":"VF Pisarenko","year":"1973","unstructured":"Pisarenko, V.F.: The retrieval of harmonics from a covariance function. Geophys. J. Roy. Astron. Soc. 33, 347\u2013366 (1973)","journal-title":"Geophys. J. Roy. Astron. Soc."},{"key":"9692_CR29","unstructured":"Plonka, G., Pototskaia, V.: Application of the AAK theory for sparse approximation of exponential sums. arXiv: 1609.09603 (2016)"},{"issue":"2","key":"9692_CR30","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1002\/gamm.201410011","volume":"37","author":"G Plonka","year":"2014","unstructured":"Plonka, G., Tasche, M.: Prony methods for recovery of structured functions. GAMM-Mitt. 37(2), 239\u2013258 (2014)","journal-title":"GAMM-Mitt."},{"key":"9692_CR31","doi-asserted-by":"crossref","unstructured":"Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Springer (2019)","DOI":"10.1007\/978-3-030-04306-3"},{"key":"9692_CR32","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1080\/00036810903569499","volume":"90","author":"D Potts","year":"2011","unstructured":"Potts, D., Tasche, M.: Nonlinear approximation by sums of nonincreasing exponentials. Appl. Anal. 90, 609\u2013626 (2011)","journal-title":"Appl. Anal."},{"issue":"4","key":"9692_CR33","doi-asserted-by":"publisher","first-page":"1024","DOI":"10.1016\/j.laa.2012.10.036","volume":"439","author":"D Potts","year":"2013","unstructured":"Potts, D., Tasche, M.: Parameter estimation for nonincreasing sums by Prony-like methods. Linear Algebra Appl. 439(4), 1024\u20131039 (2013)","journal-title":"Linear Algebra Appl."},{"key":"9692_CR34","doi-asserted-by":"publisher","first-page":"984","DOI":"10.1109\/29.32276","volume":"37","author":"R Roy","year":"1989","unstructured":"Roy, R., Kailath, T.: ESPRIT estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process 37, 984\u2013995 (1989)","journal-title":"IEEE Trans. Acoust. Speech Signal Process"},{"key":"9692_CR35","unstructured":"Schmidt, R.O.: A signal subspace approach to multiple emitter location and spectral estimation, PhD thesis, Stanford University (1981)"},{"issue":"8","key":"9692_CR36","doi-asserted-by":"publisher","first-page":"2119","DOI":"10.1109\/TIM.2013.2265436","volume":"62","author":"JA la O Serna de","year":"2013","unstructured":"de la O Serna, J.A.: Synchrophasor estimation using Prony\u2019s method. IEEE Trans. Instrument. Measur. 62(8), 2119\u20132128 (2013)","journal-title":"IEEE Trans. Instrument. Measur."},{"key":"9692_CR37","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.cam.2017.05.029","volume":"326","author":"M-R Skrzipek","year":"2017","unstructured":"Skrzipek, M.-R.: Signal recovery by discrete approximation and a Prony-like method. J. Comput. Appl Math. 326, 193\u2013203 (2017)","journal-title":"J. Comput. Appl Math."},{"issue":"1","key":"9692_CR38","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1109\/78.365329","volume":"43","author":"CW Therrien","year":"1995","unstructured":"Therrien, C.W., Velsaco, C.H.: An iterative method for ARMA signal modeling. IEEE Trans. Signal Process. 43(1), 358\u2013361 (1995)","journal-title":"IEEE Trans. Signal Process."},{"key":"9692_CR39","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1016\/j.cam.2013.04.034","volume":"272","author":"K Usevich","year":"2014","unstructured":"Usevich, K., Markovsky, I.: Variable projection for affinely structured low-rank approximation in weighted 2-norms. J. Comput. Appl. Math. 272, 430\u2013448 (2014)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09692-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-019-09692-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09692-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,17]],"date-time":"2024-07-17T04:51:00Z","timestamp":1721191860000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-019-09692-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,23]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["9692"],"URL":"https:\/\/doi.org\/10.1007\/s10444-019-09692-y","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,23]]},"assertion":[{"value":"19 June 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 April 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}