{VERSION 4 0 "HP RISC UNIX" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 39 " Procedure called by Newton procedure ;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "iterate := proc( f::procedur e, df::procedure, x0::numeric, N::posint)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " local xold, xnew ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " xold := x0 ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 " xnew := e valf( xold - f(xold) / df(xold) ) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " to N-1 while abs(xnew-xold) > 10^(1-Digits) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " xold := xnew ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " print(xold) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " xnew := evalf( xold - f(xold) / df(xold) ) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " od ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " xne w ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "end :" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Procedure to carry out Newton -Raphson iteration algorithm in one dimension ;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 53 "Newton := proc( f::procedure, x0::numeric, N:: posint)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " local df ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " df := D(f) :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " print(x0) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " \+ iterate(f, df, x0, N) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "end :" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 61 " Apply the Newton procedure to compute the square root of 2;" }}{PARA 0 "" 0 "" {TEXT -1 71 "Begin by defining a procedure t hat maps an input value x into x^2 - 2 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f := x -> x^2 - 2 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowGF(,&*$)9$\"\"#\"\"\"F1F0!\"\"F (F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Newton(f, 1.5, 15) ;" }}}}{MARK "11" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }