{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T04:10:04Z","timestamp":1742962204914,"version":"3.40.3"},"publisher-location":"Cham","reference-count":24,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031782657"},{"type":"electronic","value":"9783031782664"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-78266-4_29","type":"book-chapter","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T15:36:39Z","timestamp":1735659399000},"page":"325-341","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Method of Fitting a Nonlinear Function to Measurement Data, Its Uncertainty and as Example the Application in Thermistor Circuits"],"prefix":"10.1007","author":[{"given":"Jacek","family":"Puchalski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zygmunt L.","family":"Warsza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,1,1]]},"reference":[{"key":"29_CR1","unstructured":"Joint Committee for Guides in Metrology (BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML) JCGM 100:2008 Evaluation of Measurement Data\u2014Guide to the Expression of Uncertainty in Measurement. Sevres, France: International Bureau of Weights and Measures BIPM"},{"key":"29_CR2","doi-asserted-by":"crossref","unstructured":"Reed, B.C.: Linear least-squares fits with errors in both coordinates. II: comments on parameter variances. Am. J. Phys. 60, 59\u201362 (1992)","DOI":"10.1119\/1.17044"},{"key":"29_CR3","unstructured":"Nielssen, L.: Evaluation of measurements by the method of least squares. In: Levesley, J., Anderson, I.J., Mason, J.C. (eds.) Reprint from Algorithms for Approximation IV, University of Huddersfield, pp. 170\u2013186 (2002)"},{"key":"29_CR4","doi-asserted-by":"crossref","unstructured":"York, D., Evensen, M.N., Lopez Martines, M., DE Basabe Delgato, J.: Unified equations for the slope, intercept, and standard errors for the best straight line. AM. J. Phys. 72(3), 367\u2013375 (2004)","DOI":"10.1119\/1.1632486"},{"key":"29_CR5","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1088\/1681-7575\/aa8f02","volume":"54","author":"I Lira","year":"2017","unstructured":"Lira, I., Grientschnig, D.: Error-in-variables models in calibration. Metrologia 54, 133 (2017)","journal-title":"Metrologia"},{"key":"29_CR6","doi-asserted-by":"publisher","first-page":"035101","DOI":"10.1088\/0957-0233\/3\/035101","volume":"22","author":"M Krystek","year":"2011","unstructured":"Krystek, M., Mathias, A.: A least-squares algorithm for fitting data points with mutually correlated coordinates to a straight line. Meas. Sci. Technol. 22, 035101 (2011). https:\/\/doi.org\/10.1088\/0957-0233\/3\/035101","journal-title":"Meas. Sci. Technol."},{"key":"29_CR7","doi-asserted-by":"crossref","unstructured":"Amiri-Simkooei, A.R., et al.: Estimation of straight-line parameters with fully correlated coordinates. Measurement 48, 378\u2013386 (2014)","DOI":"10.1016\/j.measurement.2013.11.005"},{"key":"29_CR8","doi-asserted-by":"publisher","unstructured":"Davidson, W.C.: Variable Metric Method for Minimization. AEC Research and Development Report ANL 5990. https:\/\/doi.org\/10.2172\/4252678","DOI":"10.2172\/4252678"},{"key":"29_CR9","doi-asserted-by":"publisher","unstructured":"Dennis, J.E. Jr., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM 1996 reproduction of Prentice-Hall 1983 edition. https:\/\/doi.org\/10.1137\/1.9781611971200","DOI":"10.1137\/1.9781611971200"},{"key":"29_CR10","unstructured":"Fletcher, R.: Practical Methods of Optimization (2nd ed.). John Wiley and Sons, New York (1987). ISBN 978\u20130\u2013471\u201391547\u20138"},{"key":"29_CR11","doi-asserted-by":"publisher","unstructured":"Mascarenhas, W.F.: The divergence of the BFGS and Gauss Newton Methods, Mathematical Programming, 2013, arXiv:1309.7922, https:\/\/doi.org\/10.48550\/arXiv.1309.7922","DOI":"10.48550\/arXiv.1309.7922"},{"key":"29_CR12","doi-asserted-by":"publisher","unstructured":"Levenberg, K.: A method for the solution of certain non-linear problems in least squares. Q. Appl. Math. 2(2), 164\u2013168 (1944). https:\/\/doi.org\/10.1090\/qum\/10666","DOI":"10.1090\/qum\/10666"},{"key":"29_CR13","doi-asserted-by":"publisher","unstructured":"Marquardt, D.: An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11(2), 431\u2013441 (1963). https:\/\/doi.org\/10.1137\/0111030","DOI":"10.1137\/0111030"},{"key":"29_CR14","doi-asserted-by":"publisher","unstructured":"Kanzow, C.H., Yamashita, N., Fukushima, M.: Levenberg\u2013Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints. J. Comput. Appl. Math. 172(2), 375\u2013397 (2004). https:\/\/doi.org\/10.1016\/j.cam.2004.02.013","DOI":"10.1016\/j.cam.2004.02.013"},{"key":"29_CR15","doi-asserted-by":"publisher","unstructured":"Warsza, Z.L., Puchalski, J.: Method of estimation uncertainties of indirect multivariable measurement including accuracy of processing function as extension of GUM S2. In: Advanced Mathematical and Computational Tools in Metrology and Testing AMCTM XII. Pavese F., Forbes A.B., Zhang N.F., Chunovkina A.G. (eds.): Series on Advances in Mathematics for Applied Sciences, vol. 90, pp. 451\u201363, World Scientific, New Jersey, London, Singapore (2021). ISBN 978\u2013981\u2013124\u201337\u20133 0I, https:\/\/doi.org\/10.1142\/9789811242380_0029","DOI":"10.1142\/9789811242380_0029"},{"key":"29_CR16","doi-asserted-by":"publisher","unstructured":"Warsza, Z.L., Puchalski, J.: Uncertainty bands of the regression line for autocorrelated data of dependent variable Y. In: Proceedings of 22nd Conference on Automation 2021, vol. 1390, 364\u2013386 (2021). https:\/\/doi.org\/10.1007\/978-3-03074893-7_33","DOI":"10.1007\/978-3-03074893-7_33"},{"key":"29_CR17","doi-asserted-by":"crossref","unstructured":"Puchalski, J.: A new algorithm for generalization of least square method for straight line regression in cartesian system for fully correlated both coordinates. Int. J. Autom. AI Mach. Learn. 2(2), 20\u201354 (2021)","DOI":"10.61797\/ijaaiml.v2i2.98"},{"key":"29_CR18","doi-asserted-by":"crossref","unstructured":"Puchalski, J., Warsza, Z.L.: Regression and uncertainty of a straight line for measurements of x and y variables with all correlations. (in Polish) PAR (Pomiary Automatyka Robotyka) R.26. Nr 2\/2022 s.47\u201358 ISSN 427\u20139126","DOI":"10.14313\/PAR_244\/47"},{"key":"29_CR19","unstructured":"Puchalski, J., Warsza, Z.L.: Determining a straight line by the linear regression method and its uncertainty band with reference to the GUM guide from measurements of both variables x and y with their autocorrelation and cross-correlation. Monograph in Polish: METROLOGIA badania i zastosowania. Monografia M152, TU Politechnika \u015awi\u0119tokrzyska Kielces. 235\u2013256"},{"key":"29_CR20","doi-asserted-by":"publisher","unstructured":"Warsza, Z.L., Puchalski, J.: Uncertainty bands of the regression line for data with type A and type B uncertainties of dependent variable Y. In: Proceedings of 22nd Conference on Automation 2021, vol. 1390, pp. 342\u2013363 (2021). https:\/\/doi.org\/10.1007\/978-3-03074893-7_32","DOI":"10.1007\/978-3-03074893-7_32"},{"key":"29_CR21","unstructured":"Puchalski, J., Warsza, Z.L.: Linear regression method of matching the parabolic curve to tested points of both correlated coordinates Abstract 2p. Paris MathMet 2022 EMN Conference"},{"key":"29_CR22","doi-asserted-by":"publisher","unstructured":"Puchalski, J., Warsza, Z.L.: The method of fitting a non-linear function to data of measured points and its uncertainty band. (in Polish) Pomiary Automatyka Robotyka, R.26. Nr 3\/2023 s.45\u201355. https:\/\/doi.org\/10.14313\/PAR_249\/45","DOI":"10.14313\/PAR_249\/45"},{"key":"29_CR23","unstructured":"Draper, R.D., Smith, H.: Applied Regression Analysis, 3rd Edn. Willey, New York (Polish translation of ed. 1 from 1966) (1998)"},{"key":"29_CR24","doi-asserted-by":"publisher","unstructured":"Grafarend, E.W., Awange, J.L.: Applications of linear and nonlinear models\u2013fixed effects, random effects, and total least squares. J. Geodetic Sci. 3(1), 77\u201378 (2013). https:\/\/doi.org\/10.2478\/jogs-2013-0009","DOI":"10.2478\/jogs-2013-0009"}],"container-title":["Lecture Notes in Networks and Systems","Automation 2024: Advances in Automation, Robotics and Measurement Techniques"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-78266-4_29","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T15:47:52Z","timestamp":1735660072000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-78266-4_29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031782657","9783031782664"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-78266-4_29","relation":{},"ISSN":["2367-3370","2367-3389"],"issn-type":[{"type":"print","value":"2367-3370"},{"type":"electronic","value":"2367-3389"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"1 January 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"AUTOMATION","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Conference on Automation","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Warsaw","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 May 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 May 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"aarmt2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/automation.piap.pl\/en\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}