# Implementation of golden section search for extremum in R

How can we modified this code to more efficient one and search until a tolerance level is reached for p1-p2 and in result we get the extremum value? Is there any faster algorithm for finding the extremum than this golden section serach ?

lambda<-(sqrt(5)-1)/2 golden.section<-function(f, pL, pU, p1, p2, top, result){ if (top==26){ return(result) } else if(top==1){ p1<-pL + (1-lambda)*(pU - pL) p2<-pU - (1-lambda)*(pU - pL) } result[top,]<-c(p1,p2) if(f(p2) < f(p1)){ pU<-p2 pL<-pL p2<-p1 p1<-pL + (1-lambda)*(pU - pL) } else if (f(p2) > f(p1)){ pU <- pU pL <- p1 p1 <- p2 p2<-pU - (1-lambda)*(pU - pL) } result<-golden.section(f, pL, pU, p1, p2, top=top+1, result) return(result) } result<-data.frame(p1=rep(NA, 25), p2=rep(NA, 25)) result<-golden.section(function(x) -(x - 1.235)^2 + 0.78 * x + 0.2, -5, 5, NA, NA, 1, result)