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As a result, when the neural network has a big number of weights, the algorithm becomes practically ineffective. This article presents a new parallel approach to the computations in Levenberg-Marquardt neural network learning algorithm. The proposed solution is based on vector instructions to effectively reduce the high computational time of this algorithm. The new approach was tested on several examples involving the problems of classification and function approximation, and next it was compared with a classical computational method. The article presents in detail the idea of parallel neural network computations and shows the obtained acceleration for different problems.<\/jats:p>","DOI":"10.2478\/jaiscr-2023-0006","type":"journal-article","created":{"date-parts":[[2023,3,11]],"date-time":"2023-03-11T00:46:36Z","timestamp":1678495596000},"page":"45-61","source":"Crossref","is-referenced-by-count":61,"title":["Fast Computational Approach to the Levenberg-Marquardt Algorithm for Training Feedforward Neural Networks"],"prefix":"10.2478","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1769-3934","authenticated-orcid":false,"given":"Jaros\u0142aw","family":"Bilski","sequence":"first","affiliation":[{"name":"Department of Computational Intelligence , Cz\u0119stochowa University of Technology , al. 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