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{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 
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{SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 5 "Title" }}{EXCHG {PARA 18 "
" 0 "" {TEXT 256 103 "Maple Worksheet showing the Application of Nonli
near Convergence Accelerators to a Multipolar Expansion" }}}}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 25 "Bibliographic Information" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT 257 118 "Supplementary to Paper 8 at the Fourth \+
Electronic Computational Chemistry Conference, November 1 to December \+
12, 1997," }}{PARA 0 "" 0 "" {TEXT 261 36 "submitted to the Internet J
. Chem., " }}{PARA 0 "" 0 "" {TEXT 263 76 "See also http://www.chemie.
uni-regensburg.de/ECCC/4/paper.homeier/paper.html" }}}}{SECT 0 {PARA 
3 "" 0 "" {TEXT -1 20 "Author and Copyright" }}{EXCHG {PARA 19 "" 0 "
" {TEXT 258 21 "Herbert H. H. Homeier" }}{PARA 260 "" 0 "" {TEXT -1 
51 "Institut fuer Physikalische und Theoretische Chemie" }}{PARA 261 "
" 0 "" {TEXT -1 52 "Universitaet Regensburg, D-93040 Regensburg, Germa
ny" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 
-1 19 "Maple Preliminaries" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 19 "Res
tart the session" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;
" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 34 "Defining the accuracy that \+
is used" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=32;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#K" }}}}}{PARA 3 "" 0 "" 
{TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 21 "Procedure definit
ions" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 60 "Procedure implementing th
e nonlinear convergence accelerator" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 641 "KH4:=proc(n,s_n,omega_n,delta,c0_n,c1_n,c2_n,Ac0,Ac1
,Ac2,ANum,ADen)\nlocal k,kmax,m,m1,m2,mpkm1,c0,c1,c2,aux;\nkmax := flo
or(n/2); \nAc0[n]:=c0_n;\nAc1[n]:=c1_n;\nAc2[n]:=c2_n;\nADen[n]:=1/ome
ga_n;\nANum[n]:=s_n/omega_n;\nfor k from 1 to kmax do\n        m := n \+
- 2*k;\n        m1 := m+1;\n        m2 := m+2;\n        mpkm1 := m +k \+
- 1;\n        c0:=Ac0[mpkm1];\n        c1:=Ac1[mpkm1];\n        c2:=Ac
2[mpkm1];\n        aux := delta(m,k);\n        ADen[m]:=( ADen[m] * c0
 + ADen[m1] * c1 + ADen[m2] * c2 ) / aux;\n        ANum[m]:=( ANum[m] \+
* c0 + ANum[m1] * c1 + ANum[m2] * c2 ) / aux;\nod;\nk:=n mod 2;\nRETUR
N(ANum[k]/ADen[k]);\nend:\ndelta:=(n,k)->1/(n+1):\n \n" }}}}{PARA 4 "
" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 64 "Procedure \+
for doing the summation and calling of the accelerator" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 654 "main_q:=proc(nmax,x,digi)\nlocal x
x,n,summe,true_value,a_n,s_n,omega_n,c0_n,c1_n,c2_n,Ac0,Ac1,Ac2,Anum,A
den\n,\npredic_n,abs_err_n,rel_err_n,digits_n,adummy,digidum,Digitsold
;\nsumme:=0;\nxx:=x;\nadummy:=a;\ndigidum:=digi;\nDigitsold:=Digits;Di
gits:=digi:xx:=evalf(xx);adummy:=evalf(adummy);\nfor n from 0 to nmax \+
do\n        a_n := evalf(qq[n]/adummy**(n+1),digidum);\n        summe \+
:= summe + a_n*orthopoly[P](n,xx);\n        s_n := summe;\n        ome
ga_n := a_n;\n        c0_n := n+2;\n        c1_n := -(2*n+5)*xx;\n    \+
    c2_n := n+3;\n        predic_n := KH4(n,s_n,omega_n,delta,c0_n,c1_
n,c2_n,Ac0,Ac1,Ac2,ANum,ADen\n);\nod;\nDigits:=Digitsold;RETURN(predic
_n):end:\n\n" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 55 "Procedure for c
alling the main one for various maximal " }{TEXT 259 1 "l" }{TEXT -1 
7 "-values" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "comput:=n->mai
n_q(n,x,32);" }}{PARA 0 "" 0 "" {XPPMATH 20 "6#>%'computG:6#%\"nG6\"6$
%)operatorG%&arrowGF(-%'main_qG6%9$%\"xG\"#KF(F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'computG:6#%\"nG6\"6$%)operatorG%&arrowGF(-%'main_qG6
%9$%\"xG\"#KF(F(" }}}}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 
3 "" 0 "" {TEXT -1 49 "Table defining the multipole coefficients (up t
o " }{TEXT 262 1 "l" }{TEXT -1 4 "=30)" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3420 "qq := table([(10)=2536.0253549353621841734265628560
622957923718744799585608259\\\n087327999286788800683527793299165416828
6920808411907758,(26)=63243038.87231813\\\n835506979886979111387709277
333426689703741126653639828503,(5)=130.141600819240\\\n744739542519345
018069368745615526146965577625783668836344735092103517131720204\\\n138
4017725298065011779092738973,(23)=9119803.3217610020224481803937771218
71384\\\n096341170759098793280334840047266599758353,(11)=4676.09090109
75209906760704031\\\n0718675348880715438612867057665152860598889615942
19271056489323196959656867063\\\n82348,(13)=16092.05536294542638950198
19593319157713487339730878181804688345142\\\n2956173621819933788124675
32696944932818795,(27)=120907778.65352851781634131979\\\n6344298459713
75886653144710074842555797033,(24)=17367785.134246280219163388864\\\n1
55276263107358328326969554723229420267103802474029,(16)=105263.9883272
0894492\\\n00506164958833427925729994583064310179447275816082819543581
6669279021564850615\\\n912,(17)=197913.2716284260335114751682535483063
3302216727715227241298727845337\\\n418610728626518599345007948250,(9)=
1381.97580244714368993441950070935936515922\\\n17467724909608706395413
2416265627869580169483999641396522354377987752029675,(2\n)=24.97214081
99329059332878025150856463820191750127426834578265821981429265030\\\n2
1277236460004398138258171699714781050938171870326255,(0)=9.61455428369
5725384\\\n92738536504204187653904800745722620430883204363255555048168
6533860775410100693\\\n6037673064304695790447351293290,(3)=42.50809421
5318605089568757444399677874716\\\n35100654243834088605232798194777190
9345627853008780156198070146985320368023448\\\n66624486,(15)=56126.132
1390823154944483087575877621256181360633390350142261235\\\n42318453096
96456587602594134680261988690,(28)=231416232.6944333801967099966319\\
\n9730514595770638351694659615852452209,(22)=4795800.10736524845293177
2636848539\\\n677367077923553510032053026187257103259789591869357,(21)
=2525892.1378457704386\\\n55412971212128517844655089484981127261672824
598797192112019128845701,(19)=\n704298.1989868574787279622075559056487
1976862600057991475932814554442085216681\\\n9432029003464937,(14)=3000
7.86826120760907652951868097846889277913704393533614\\\n75644138510046
036956690933507607116328482349787905,(8)=757.2446085940212871430\\\n98
4730794298545488000046693054454493380150039610188404584947655157899788
878730\\\n775759329547061201,(4)=73.8292804795366600451243768864779007
862009641387486783\\\n494315185052556098017781413928496774416910349403
98891165902925581072404,(20)=\n1332585.8332275628545892148492412669973
991254439708597464104443670956224057344\\\n11333267232064,(12)=8658.39
408088280428762690268923014897267452338590561765883\\\n550904317460650
61193147655339943474666185228932824498,(18)=372958.142855604674\\\n100
8480845241215644674539931448090698966842735446226620093191585458419010
4429,\n(7)=417.5980141551773043314753605341032387766799791710411271418
929718490769434\\\n15899059715972514474945897569316972915819849791,(25
)=33120638.6231272867835201\\\n709816488066832487548541242727679974274
34321440044424,(1)=15.11146816206042911\\\n876060236327741617885309833
173463188735341660766278988806029912084852624560179\\\n874144096404836
8385779972470357,(29)=443409058.5980392849974617381663695899027\\\n520
5214911734903765297776,(6)=232.052203428566183244396565991130906651299
00471\\\n5356157724001983371889398408307998134780618635337501053327642
79372774027277,(\n30)=850475486.17268163983656466870923774674944616083
998921960406829]):\n" }}}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 59 "Setting distance and angle (in degrees) t
o expansion center" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "a:=3;t
heta:=45*degrees;x:=cos(Pi/180*theta/degrees):" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"aG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&theta
G,$%(degreesG\"#X" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 109 "Doing tes
t calculations in the given geometry with various accuracies, rounded \+
later for display to 16 digits" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 29 
"with multipolmoments up to 30" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 68 "main_q(30,x,16);evalf(main_q(30,x,32),16);evalf(main_q(30,x,64),
16);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"15pn)*)Q$\\V!#:" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"1[Tz)*)Q$\\V!#:" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"1[Tz)*)Q$\\V!#:" }}}}{PARA 3 "" 0 "" {TEXT -1 0 "" }
}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 29 "with multipolmoments up to 21" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "main_q(21,x,16);evalf(main_
q(21,x,32),16);evalf(main_q(21,x,64),16);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"15<y)*)Q$\\V!#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$
\"1'*fx)*)Q$\\V!#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"1'*fx)*)Q$\\V
!#:" }}}{PARA 5 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT -1 21 "with varying maximal " }{TEXT 260 1 "l" }{TEXT -1 7 "-val
ues" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "for l from 0 to 30 by
 5 do l,comput(l);od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$\"\"!$\"AS,b%G\"4$G^d)*yU^[?$!#J" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$\"\"&$\"A8jX+yT2`-o3<A^[V!#J" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$\"#5$\"A&fMmnv8xFEwW;P$\\V!#J" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"#:$\"Ag`d$*GB-)\\*f?)))Q$\\V!#J" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"#?$\"A;,&>y!=w(zJf()*)Q$\\V!#J" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"#D$\"AMnDXQNu:*>%z)*)Q$\\V!#J" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"#I$\"AMX!fW4ymy9%z)*)Q$\\V!#J" }}}}}{PARA 3 "" 0 "" 
{TEXT -1 0 "" }}}{MARK "1 1 2 0" 76 }{VIEWOPTS 1 1 0 2 1 1805 }