{"title":"基于Bernstein多项式的最佳神经网络逼近与GRNN学习应用","authors":"H. A. Almurieb, Anwar Anwer Hamody","doi":"10.55810/2312-5721.1003","DOIUrl":null,"url":null,"abstract":"Bernstein polynomials are one of the fi rst and main tools for function approximation. On the other hand, neural networks have many useful applications in approximation and other fi elds as well. In this paper, we study how we bene fi t from properties of Bernstein polynomials to de fi ne a new version of neural networks, that can be fi t approxi-mating functions in terms of modulus of continuity. Numerically, we use neural networks to approximate some types of continuous functions. For that purpose, we use GRNN algorithm to approximate functions uniformly by using Matlab, giving some examples that con fi rm good rate approximation.","PeriodicalId":218143,"journal":{"name":"Al-Bahir Journal for Engineering and Pure Sciences","volume":"115 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Best Neural Network Approximation by using Bernstein Polynomials with GRNN Learning Application\",\"authors\":\"H. A. Almurieb, Anwar Anwer Hamody\",\"doi\":\"10.55810/2312-5721.1003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Bernstein polynomials are one of the fi rst and main tools for function approximation. On the other hand, neural networks have many useful applications in approximation and other fi elds as well. In this paper, we study how we bene fi t from properties of Bernstein polynomials to de fi ne a new version of neural networks, that can be fi t approxi-mating functions in terms of modulus of continuity. Numerically, we use neural networks to approximate some types of continuous functions. For that purpose, we use GRNN algorithm to approximate functions uniformly by using Matlab, giving some examples that con fi rm good rate approximation.\",\"PeriodicalId\":218143,\"journal\":{\"name\":\"Al-Bahir Journal for Engineering and Pure Sciences\",\"volume\":\"115 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Al-Bahir Journal for Engineering and Pure Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55810/2312-5721.1003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Al-Bahir Journal for Engineering and Pure Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55810/2312-5721.1003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Best Neural Network Approximation by using Bernstein Polynomials with GRNN Learning Application
Bernstein polynomials are one of the fi rst and main tools for function approximation. On the other hand, neural networks have many useful applications in approximation and other fi elds as well. In this paper, we study how we bene fi t from properties of Bernstein polynomials to de fi ne a new version of neural networks, that can be fi t approxi-mating functions in terms of modulus of continuity. Numerically, we use neural networks to approximate some types of continuous functions. For that purpose, we use GRNN algorithm to approximate functions uniformly by using Matlab, giving some examples that con fi rm good rate approximation.