{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {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 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warni ng" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2861 "################## ###################\n# Maple V, Release 4 script for the #\n# calculat ion of Schroder's methods #\n# #\n# \+ Copyright (C) 1996 by Dann Corbit #\n# [ Generic version ] \+ #\n# \"MaximumTerm\" controls the number #\n# of algorithms generat ed. #\n#####################################\n#>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>\n# Reference:\n# \"On In finitely Many Algorithms For Solving Equations\"\n# by Ernst Schrod er, Translated by G. W. Stuart.\n# Synopsis:\n# Local convergence rat es can be made arbitrarily large.\n# Ernst Schroder showed, over 100 \+ years ago, how a family\n# of explicit single-point formulas could be designed to\n# have arbitrarily high orders of (local) convergence. \n# You can obtain a translation of Schroder's paper at:\n# ftp:// thales.cs.umd.edu/pub/reports/imase.ps\n# Web surfers may find it eas ier to pick it up via\n# Mr. Stuart's home page. The URL is:\n# h ttp://www.cs.umd.edu/~stewart/\n#<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< <<<<<<<<<<<<<<<<<<<<\n\n# Generic definition of y as some function of \+ x\ny := exp(x)-c;\nreadlib(C):\n# Definition of the first term for Sch roder's Series 'A'\n# Equation 55, Page 30.\nA(0, 0) := 1/y;\n\n# Defi nition of the first term for Schroder's Series 'B'\n# Equation 56, Pag e 31.\nB(0, 0) := diff(y, x)/y;\n\n# We can change MaximumTerm to proc ess as many terms as we like\nMaximumTerm := 10;\n# Iterate to create \+ terms from 1 to MaximumTerm\nfor i from 1 to MaximumTerm do w := i;\n \n # Definition of the Lamda=0 terms for Schroder's Series 'A'\n # Equation 55, Page 30.\n A(0, w) := simplify(sum('(-1)^(a-1)*y^(a-1) *diff(y, x$a)*y^(w-a+1)*A(0, w-a)/a!', 'a'=1..w)/y^(w+1));\n\n # Def inition of the Lamda=0 terms for Schroder's Series 'B'\n # Equation \+ 55, Page 30.\n B(0, w) := simplify(sum('(-1)^(a)*y^(a)*diff(y, x$(a+ 1))*y^(w-a+1)*A(0, w-a)/a!', 'a'=0..w)/y^(w+1));\n\n # Definition of the Omega=0 terms for Schroder's Series 'A'\n # Equation 70, Page 4 0.\n A(l, 0) := simplify(x^l*y*A(0, 0)/y);\n\n # Definition of the Omega=0 terms for Schroder's Series 'B'\n # Equation 70, Page 40.\n B(l, 0) := simplify(x^l*y*B(0, 0)/y);\n\n # Definition of the Lam da, Omega terms for Schroder's Series 'A'\n # Equation 70, Page 40. \n A(l, w) := simplify(sum('(-1)^(a)*l!/(a!*(l-a)!)*x^(l-a)*y^a*y^(w -a+1)*A(0, w-a)', 'a'=0..w)/y^(w+1));\n\n # Definition of the Lamda, Omega terms for Schroder's Series 'B'\n # Equation 70, Page 40.\n \+ B(l, w) := simplify(sum('(-1)^(a)*l!/(a!*(l-a)!)*x^(l-a)*y^a*y^(w-a+1 )*B(0, w-a)', 'a'=0..w)/y^(w+1));\n\n # Definition of the Algorithm \+ based on A(Lamda, Omega) Page 39.\n xprimeA := x - simplify(A(l, w-1 )/A(l, w));\n\n # Definition of the Algorithm based on B(Lamda, Omeg a) Page 39.\n xprimeB := x - simplify(B(l, w-1)/B(l, w)); C(xprimeB, optimized);\nod;\nl:= 0; \n C(xprimeB, optimized);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&-%$expG6#%\"xG\"\"\"%\"cG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!F'*$,&-%$expG6#%\"xG\"\"\"%\"c G!\"\"F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!F'*&-%$expG6 #%\"xG\"\"\",&F)F-%\"cG!\"\"F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,M aximumTermG\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"\"*&-%$expG6#%\"xGF( ,&F*!\"\"%\"cGF(!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"! \"\"\"*(-%$expG6#%\"xGF(%\"cGF(,&F*!\"\"F.F(!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!F'*$,&-%$expG6#%\"xG\"\"\"%\"cG!\"\"F0" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!F',$*&-%$expG6#%\"xG\" \"\",&F*!\"\"%\"cGF.F0F0" }}{PARA 8 "" 1 "" {TEXT -1 64 "Error, (in su m) the argument to factorial should be non-negative" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"lG\"\"!" }}{PARA 6 "" 1 "" {TEXT -1 3054 " t 1 = log(x);\n t2 = t1*t1;\n t3 = t2*t2;\n t4 = t3*t1;\n t5 = c*c;\n t6 = t3*t5;\n t7 = t5*t5;\n t8 = t7*c ;\n t9 = t1*t8;\n t10 = t2*t7;\n t11 = t4*c;\n t12 = t2*t1;\n t13 = t12*t5;\n t14 = t3*t12;\n t15 = 64638 00.0*t4+4384800.0*t5+7592760.0*t3+65131200.0*t6+4384800.0*t2\n-2605248 0.0*t9+65131200.0*t10+1814400.0*t1-6463800.0*t8-26052480.0*t11\n-18144 00.0*c+64638000.0*t13+2345400.0*t14;\n t16 = t14*t5;\n t17 = t12*c;\n t18 = t5*c;\n t19 = t1*t18;\n t20 = t2*t5;\n \+ t21 = t2*c;\n t22 = t1*t5;\n t23 = t1*c;\n t24 = t 3*t3;\n t25 = t24*c;\n t26 = t3*t2;\n t27 = t26*t18;\n \+ t28 = t3*t8;\n t29 = t7*t5;\n t30 = t12*t29;\n t31 = t2*t8;\n t32 = t1*t29;\n t33 = t4*t5;\n t34 = 130636 80.0*t16-30371040.0*t17-30371040.0*t19+45556560.0*t20\n-20412000.0*t21 +20412000.0*t22-8769600.0*t23-3265920.0*t25-30481920.0*t27\n-45722880. 0*t28+30481920.0*t30-49253400.0*t31+16417800.0*t32+49253400.0*t33;\n \+ t36 = t3*t18;\n t37 = t12*t7;\n t38 = t2*t18;\n t39 = t1*t7;\n t40 = t3*c;\n t41 = t7*t18;\n t42 = t1*t41; \n t43 = t12*t8;\n t44 = t26*c;\n t45 = t14*c;\n t 46 = -82089000.0*t36+82089000.0*t37+7592760.0*t7-64638000.0*t38+\n3231 9000.0*t39-32319000.0*t40-8212608.0*t42-2345400.0*t41+1026576.0*t24+\n 6804000.0*t12-6804000.0*t18-57488256.0*t43-16417800.0*t44-8212608.0*t4 5;\n t47 = t26*t5;\n t48 = t4*t18;\n t49 = t3*t7;\n \+ t50 = t24*t1;\n t51 = t7*t7;\n t52 = t1*t51;\n t53 = \+ t2*t41;\n t54 = t4*t7;\n t55 = t51*c;\n t56 = t2*t29;\n t57 = t12*t18;\n t58 = 28744128.0*t47-57488256.0*t48+718603 20.0*t49+4342080.0*t26+362880.0\n*t50+1026576.0*t51+3265920.0*t52-1306 3680.0*t53+4342080.0*t29+45722880.0*t54\n-362880.0*t55+28744128.0*t56+ 362880.0-86841600.0*t57;\n t63 = 108246600.0*t4+53222400.0*t5+113 596560.0*t3+1230094800.0*t6+\n53222400.0*t2-492037920.0*t9+1230094800. 0*t10+19958400.0*t1-108246600.0*t8\n-492037920.0*t11-19958400.0*c+1082 466000.0*t13+50457000.0*t14+382631040.0*t16\n-454386240.0*t17-45438624 0.0*t19;\n t64 = 681579360.0*t20-274428000.0*t21+274428000.0*t22- 106444800.0*t23\n-95657760.0*t25-892805760.0*t27-1339208640.0*t28+8928 05760.0*t30-1059597000.0*\nt31+353199000.0*t32+1059597000.0*t33-176599 5000.0*t36+1765995000.0*t37+\n113596560.0*t7-1082466000.0*t38+54123300 0.0*t39-541233000.0*t40;\n t66 = -204057216.0*t42-50457000.0*t41+ 25507152.0*t24+91476000.0*t12\n-91476000.0*t18-1428400512.0*t43-353199 000.0*t44-204057216.0*t45+714200256.0*\nt47-1428400512.0*t48+178550064 0.0*t49+82006320.0*t26+3628800.0+10628640.0*t50+\n25507152.0*t51+95657 760.0*t52;\n t78 = -382631040.0*t53+82006320.0*t29+1339208640.0*t 54-10628640.0*t55+\n714200256.0*t56+3628800.0*t51*t5-36288000.0*t1*t55 +163296000.0*t2*t51+\n762048000.0*t26*t7-435456000.0*t14*t18-36288000. 0*t50*c+163296000.0*t24*t5\n-914457600.0*t4*t8+762048000.0*t3*t29-4354 56000.0*t12*t41+3628800.0*t24*t2\n-1640126400.0*t57;\n t84 = x+10 .0*x*(t15+t34+t46+t58)*(-t1+c)/(t63+t64+t66+t78);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 2838 }{VIEWOPTS 1 1 0 1 1 1803 }