{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T16:15:30Z","timestamp":1771949730711,"version":"3.50.1"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,10,6]],"date-time":"2010-10-06T00:00:00Z","timestamp":1286323200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2011,2]]},"DOI":"10.1007\/s00521-010-0452-y","type":"journal-article","created":{"date-parts":[[2010,10,4]],"date-time":"2010-10-04T21:14:09Z","timestamp":1286226849000},"page":"1-7","source":"Crossref","is-referenced-by-count":196,"title":["Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation"],"prefix":"10.1007","volume":"20","author":[{"given":"Yunong","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Chenfu","family":"Yi","sequence":"additional","affiliation":[]},{"given":"Dongsheng","family":"Guo","sequence":"additional","affiliation":[]},{"given":"Jinhuan","family":"Zheng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,10,6]]},"reference":[{"key":"452_CR1","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.amc.2004.10.040","volume":"169","author":"JR Sharma","year":"2005","unstructured":"Sharma JR (2005) A composite third order newton-steffensen method for solving nonlinear equations. Appl Math Comput 169:242\u2013246","journal-title":"Applied Mathematics and Computation"},{"key":"452_CR2","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s00211-006-0025-2","volume":"104","author":"C Chun","year":"2006","unstructured":"Chun C (2006) Construction of Newton-like iteration methods for solving nonlinear equations. Numerische Mathematik 104:297\u2013315","journal-title":"Numerische Mathematik"},{"key":"452_CR3","doi-asserted-by":"crossref","first-page":"1416","DOI":"10.1016\/j.amc.2005.05.036","volume":"174","author":"N Ujevic","year":"2006","unstructured":"Ujevic N (2006) A method for solving nonlinear equations. Appl Math Comput 174:1416\u20131426","journal-title":"Applied Mathematics and Computation"},{"key":"452_CR4","doi-asserted-by":"crossref","unstructured":"Zhang Y, Leithead WE, Leith DJ (2005) Time-series Gaussian process regression based on Toeplitz computation of O(N 2) operations and O(N)-level storage. In: Proceedings of the 44th IEEE conference on decision and control, pp 3711\u20133716","DOI":"10.1109\/CDC.2005.1582739"},{"key":"452_CR5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s00521-006-0074-6","volume":"17","author":"B Guo","year":"2008","unstructured":"Guo B, Wang D, Shen Y, Li Z (2008) A Hopfield neural network approach for power optimization of real-time operating systems. Neural Comput Appl 17:11\u201317","journal-title":"Neural Computing and Applications"},{"key":"452_CR6","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s005210050033","volume":"8","author":"A Wu","year":"1999","unstructured":"Wu A, Tam PKS (1999) A neural network methodology and strategy of quadratic optimization. Neural Comput Appl 8:283\u2013289","journal-title":"Neural Computing and Applications"},{"key":"452_CR7","unstructured":"Zhang Y (2005) Revisit the analog computer and gradient-based neural system for matrix inversion. In: Proceedings of IEEE international symposium on intelligent control, Limassol, Cyprus, pp 1411\u20131416"},{"key":"452_CR8","unstructured":"Zhang Y, Chen K (2008) Comparison on Zhang neural network and gradient neural network for time-varying linear matrix equation AXB\u00a0=\u00a0C solving. In: Proceedings of IEEE international conference on industrial technology, Chendu, pp 1\u20136"},{"key":"452_CR9","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1109\/TNN.2002.1031938","volume":"13","author":"Y Zhang","year":"2002","unstructured":"Zhang Y, Jiang D, Wang J (2002) A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Trans Neural Netw 13:1053\u20131063","journal-title":"IEEE Transactions on Neural Networks"},{"key":"452_CR10","doi-asserted-by":"crossref","first-page":"1477","DOI":"10.1109\/TNN.2005.857946","volume":"16","author":"Y Zhang","year":"2005","unstructured":"Zhang Y, Ge SS (2005) Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans Neural Netw 16:1477\u20131490","journal-title":"IEEE Transactions on Neural Networks"},{"key":"452_CR11","doi-asserted-by":"crossref","unstructured":"Zhang Y, Chen Z, Chen K, Cai B (2008) Zhang neural network without using time-derivative information for constant and time-varying matrix inversion. In: Proceedings of international joint conference on neural networks, Hong Kong, pp 142\u2013146","DOI":"10.1109\/IJCNN.2008.4633780"},{"key":"452_CR12","unstructured":"Zhang Y, Guo X, Ma W (2008) Modeling and simulation of Zhang neural network for online linear time-varying equations solving based on MATLAB Simulink. In: Proceedings of the seventh international conference on machine learning and cybernetics, Kunming, pp 12\u201315"},{"key":"452_CR13","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.neucom.2005.11.006","volume":"70","author":"Y Zhang","year":"2006","unstructured":"Zhang Y (2006) A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network. Neurocomputing 70:513\u2013524","journal-title":"Neurocomputing"},{"key":"452_CR14","doi-asserted-by":"crossref","first-page":"3074","DOI":"10.1109\/78.277813","volume":"41","author":"RJ Steriti","year":"1993","unstructured":"Steriti RJ, Fiddy MA (1993) Regularized image reconstruction using SVD and a neural network method for matrix inversion. IEEE Trans Signal Process 41:3074\u20133077","journal-title":"IEEE Transactions on Signal Processing"},{"key":"452_CR15","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1109\/TCS.1986.1085953","volume":"33","author":"D Tank","year":"1986","unstructured":"Tank D, Hopfield J (1986) Simple neural optimization networks: an A\/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans Circuits Syst 33:533\u2013541","journal-title":"IEEE Transactions on Circuits and Systems"},{"key":"452_CR16","doi-asserted-by":"crossref","unstructured":"Zhang Y, Peng H (2007) Zhang neural network for linear time-varying equation solving and its robotic application. In: Proceedings of the sixth international conference on machine learning and cybernetics, Hong Kong, pp 19\u201322","DOI":"10.1109\/ICMLC.2007.4370761"},{"key":"452_CR17","volume-title":"Neural Networks for Optimization and Signal Processing","author":"A Cichocki","year":"1993","unstructured":"Cichocki A, Unbehauen R (1993) Neural networks for optimization and signal processing. Wiley, Chichester"},{"key":"452_CR18","unstructured":"Zhang Y, Ma W, Yi C (2008) The link between Newton iteration for matrix inversion and Zhang neural network. In: Proceedings of IEEE international conference on industrial technology, Chendu, pp 1\u20136"},{"key":"452_CR19","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1109\/TCSI.2008.2007065","volume":"56","author":"Y Zhang","year":"2009","unstructured":"Zhang Y, Ma W, Cai B (2009) From Zhang neural network to Newton iteration for matrix inversion. IEEE Trans Circuits Syst I Regul Pap 56:1405\u20131415","journal-title":"IEEE Transactions on Circuits and Systems-I: Regular Papers"},{"key":"452_CR20","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1109\/TAC.1968.1098973","volume":"13","author":"RK Manherz","year":"1968","unstructured":"Manherz RK, Jordan BW, Hakimi SL (1968) Analog methods for computation of the generalized inverse. IEEE Trans Automat Contr 13:582\u2013585","journal-title":"IEEE Transactions on Automatic Control"},{"key":"452_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-1639-8","volume-title":"Analog VLSI and Neural Systems","author":"C Mead","year":"1989","unstructured":"Mead C (1989) Analog VLSI and neural systems. Addison-Wesley, Reading"},{"key":"452_CR22","first-page":"41","volume-title":"Progress in neurocomputing research.","author":"Y Zhang","year":"2007","unstructured":"Zhang Y (2007) Dual neural networks: design, analysis, and application to redundant robotics. In: Kang GB (eds) Progress in neurocomputing research. Nova Science Publishers, New York, pp 41\u201381"},{"key":"452_CR23","volume-title":"Numerical Methods Using MATLAB, Fourth Edition","author":"JH Mathews","year":"2004","unstructured":"Mathews JH, Fink, KD (2004) Numerical methods using MATLAB, 4th edn. Prentice Hall, New Jersey"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-010-0452-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-010-0452-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-010-0452-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T02:44:02Z","timestamp":1559702642000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-010-0452-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,6]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,2]]}},"alternative-id":["452"],"URL":"https:\/\/doi.org\/10.1007\/s00521-010-0452-y","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,6]]}}}