{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 2860 "################## ###################\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 := log(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 := 6;\n# Iterate to create t erms 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 # E quation 55, Page 30.\n A(0, w) := simplify(sum('(-1)^(a-1)*y^(a-1)*d iff(y, x$a)*y^(w-a+1)*A(0, w-a)/a!', 'a'=1..w)/y^(w+1));\n\n # Defin ition of the Lamda=0 terms for Schroder's Series 'B'\n # Equation 55 , Page 30.\n B(0, w) := simplify(sum('(-1)^(a)*y^(a)*diff(y, x$(a+1) )*y^(w-a+1)*A(0, w-a)/a!', 'a'=0..w)/y^(w+1));\n\n # Definition of t he Omega=0 terms for Schroder's Series 'A'\n # Equation 70, Page 40. \n A(l, 0) := simplify(x^l*y*A(0, 0)/y);\n\n # Definition of the O mega=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 Lamda , 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, Om ega 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 bas ed 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, Omega) \+ Page 39.\n xprimeB := x - simplify(B(l, w-1)/B(l, w)); C(xprimeB, op timized);\nod;\nl:= 0; \n C(xprimeB, optimized);\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"yG,&-%#lnG6#%\"xG\"\"\"%\"cG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!F'*$,&-%#lnG6#%\"xG\"\"\"%\"cG!\"\"F 0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!F'*&%\"xG!\"\",&-%# lnG6#F)\"\"\"%\"cGF*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,MaximumTe rmG\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"\"*&%\"xG!\"\",&-%#lnG6#F*F+% \"cGF(!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"\",$*( ,(!\"\"F(-%#lnG6#%\"xGF,%\"cGF(F(F0!\"#,&F-F,F1F(F2F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!F',$*$,&-%#lnG6#%\"xG!\"\"%\"cG\"\" \"F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!F',$*&%\"xG!\" \",&-%#lnG6#F*F+%\"cG\"\"\"F+F+" }}{PARA 8 "" 1 "" {TEXT -1 64 "Error, (in sum) the argument to factorial should be non-negative" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG\"\"!" }}{PARA 6 "" 1 "" {TEXT -1 3058 " t1 = log(x);\n t2 = t1*t1;\n t3 = c*c;\n t4 = t3*t3;\n t5 = t4*c;\n t6 = t2*t5;\n t7 = t2*t2;\n \+ t8 = t7*t1;\n t9 = t8*t4;\n t10 = t1*c;\n t11 = t3*c ;\n t12 = t2*t1;\n t13 = t12*t11;\n t14 = t8*c;\n \+ t15 = t2*t4;\n t16 = -49253400.0*t6-6463800.0*t5+1814400.0*t1+457 22880.0*t9-8769600.0*\nt10-6804000.0*t11+6804000.0*t12-86841600.0*t13+ 6463800.0*t8-26052480.0*t14+\n65131200.0*t15+4384800.0*t3+7592760.0*t7 ;\n t17 = t7*t3;\n t18 = t1*t5;\n t19 = t1*t4;\n t 20 = t12*t3;\n t21 = t2*t11;\n t22 = t4*t11;\n t23 = t1 *t22;\n t24 = t7*t7;\n t25 = t7*t12;\n t26 = t25*t3;\n \+ t27 = t24*c;\n t28 = 65131200.0*t17+7592760.0*t4+4384800.0*t 2-1814400.0*c-26052480.0*t18\n+32319000.0*t19+64638000.0*t20-64638000. 0*t21-8212608.0*t23-2345400.0*t22+\n1026576.0*t24+2345400.0*t25+130636 80.0*t26-3265920.0*t27;\n t30 = t12*c;\n t31 = t7*t2;\n \+ t32 = t31*t11;\n t33 = t1*t3;\n t34 = t2*c;\n t35 = t2 *t3;\n t36 = t7*c;\n t37 = t1*t11;\n t38 = t8*t3;\n \+ t39 = t24*t1;\n t40 = t4*t4;\n t41 = t1*t40;\n t42 = \+ t4*t3;\n t43 = t12*t42;\n t44 = t2*t22;\n t45 = -303710 40.0*t30-30481920.0*t32+20412000.0*t33-20412000.0*t34+\n45556560.0*t35 -32319000.0*t36-30371040.0*t37+49253400.0*t38+362880.0*t39+\n1026576.0 *t40+3265920.0*t41+30481920.0*t43+4342080.0*t42-13063680.0*t44;\n \+ t46 = t7*t5;\n t47 = t12*t5;\n t48 = t31*c;\n t49 = t1 2*t4;\n t50 = t7*t11;\n t51 = t40*c;\n t52 = t7*t4;\n \+ t53 = t8*t11;\n t54 = t25*c;\n t55 = t31*t3;\n t56 \+ = t2*t42;\n t57 = t1*t42;\n t58 = -45722880.0*t46+4342080.0* t31-57488256.0*t47-16417800.0*t48+\n82089000.0*t49-82089000.0*t50-3628 80.0*t51+71860320.0*t52-57488256.0*t53\n-8212608.0*t54+362880.0+287441 28.0*t55+28744128.0*t56+16417800.0*t57;\n t63 = -1059597000.0*t6- 108246600.0*t5+19958400.0*t1+1339208640.0*t9\n-106444800.0*t10-9147600 0.0*t11+91476000.0*t12-1640126400.0*t13+108246600.0*t8\n-492037920.0*t 14+1230094800.0*t15+53222400.0*t3+113596560.0*t7+1230094800.0*t17\n+11 3596560.0*t4+53222400.0*t2;\n t64 = -19958400.0*c-492037920.0*t18 +541233000.0*t19+1082466000.0*t20\n-1082466000.0*t21-204057216.0*t23-5 0457000.0*t22+25507152.0*t24+50457000.0*t25+\n382631040.0*t26-95657760 .0*t27-454386240.0*t30+3628800.0-892805760.0*t32+\n274428000.0*t33-274 428000.0*t34+681579360.0*t35;\n t68 = -541233000.0*t36-454386240. 0*t37+1059597000.0*t38+10628640.0*t39+\n762048000.0*t31*t4-36288000.0* t39*c+25507152.0*t40+95657760.0*t41+892805760.0*\nt43+82006320.0*t42-3 82631040.0*t44-1339208640.0*t46+82006320.0*t31-1428400512.0\n*t47-3531 99000.0*t48+1765995000.0*t49;\n t78 = -1765995000.0*t50-10628640. 0*t51+1785500640.0*t52-1428400512.0*t53\n-204057216.0*t54+3628800.0*t4 0*t3+3628800.0*t24*t2+163296000.0*t2*t40\n-435456000.0*t12*t22+7620480 00.0*t7*t42-914457600.0*t8*t5+163296000.0*t24*t3\n-435456000.0*t25*t11 -36288000.0*t1*t51+714200256.0*t55+714200256.0*t56+\n353199000.0*t57; \n t84 = x+10.0*x*(t16+t28+t45+t58)*(-t1+c)/(t63+t64+t68+t78);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }