{"title":"A Modified Quadratic Interpolation Method for Root Finding","authors":"V. V. Bogdanov, Yu. S. Volkov","doi":"10.1134/S1990478923030031","DOIUrl":null,"url":null,"abstract":"<p> A modification of the quadratic interpolation method for finding the root of a continuous\nfunction is proposed. Two quadratic interpolation polynomials are simultaneously constructed. It\nis shown that if the third derivative of the original function does not change sign on the considered\ninterval of localization of the required root, then the root lies between the roots of the quadratic\nfunctions. This allows one to substantially narrow the localization interval and reduce the number\nof steps to calculate the root with a given accuracy. The proposed modification of the quadratic\ninterpolation method is used in the problem of calculating isolines when modeling the hill diagram\nof hydraulic turbines.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 3","pages":"491 - 497"},"PeriodicalIF":0.5800,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923030031","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
A modification of the quadratic interpolation method for finding the root of a continuous
function is proposed. Two quadratic interpolation polynomials are simultaneously constructed. It
is shown that if the third derivative of the original function does not change sign on the considered
interval of localization of the required root, then the root lies between the roots of the quadratic
functions. This allows one to substantially narrow the localization interval and reduce the number
of steps to calculate the root with a given accuracy. The proposed modification of the quadratic
interpolation method is used in the problem of calculating isolines when modeling the hill diagram
of hydraulic turbines.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
