Romberg.xls

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1		Romberg (Richardson) Iteration
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5							function evaluations
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10	Example 1					a =	0	b =	3.141592654	b-a =	3.141592654
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12	l			Odd Sum	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32
13	1	I(1,2)	0.3265364749475	0.2078795764	0.2078795764
14	2	I(1,4)	0.4691153840404	0.3894166817	0.3223969419	0.06701973971
15	3	I(1,8)	0.5082699842300	0.6970026286	0.2584000637	0.2844292219	0.1296821269	0.02449121613
16	4	I(1,16)	0.5182596763010	1.345175971	0.1603105867	0.3082608717	0.311514862	0.2481185786	0.1675375809	0.09590420254	0.04326962995	0.01025965823
17	5	I(1,32)	0.5207693289832	2.66503797	0.08885160284	0.2162289448	0.2885378335	0.319081224	0.3194879755	0.2995197348	0.2670588454	0.2282192566	0.187533459	0.1481789117	0.1122167876	0.08082391115	0.05450540241	0.03328082039	0.01684061865	0.004672641211
18	6	I(1,64)	0.5213975010913	5.317309844	0.046717231	0.1266383316	0.1900986123	0.2389237195	0.2748695679	0.2996040889	0.3146937707	0.3215943696	0.3216452136	0.3160665544	0.3059594738	0.2923078877	0.2759822411	0.2577445273	0.2382543064	0.2180754421	0.1976833083	0.1774722585	0.1577631784	0.1388109766	0.1208118918	0.1039105237	0.08820651188	0.07376080998	0.06060151741	0.04872924539	0.03812200676	0.02873962886	0.02052769757	0.01342104703	0.007346815094	0.00222708863
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21				Table of I(P,2^l)
22		P
23	l	1	2	3	4	5	6
24	1	0.3265364749475
25	2	0.4691153840404	0.5166416870714
26	3	0.5082699842300	0.5213215176265	0.5216335063302
27	4	0.5182596763010	0.5215895736580	0.5216074440601	0.5216070303733
28	5	0.5207693289832	0.5216058798773	0.5216069669586	0.5216069593855	0.5216069591071
29	6	0.5213975010913	0.5216068917940	0.5216069592551	0.5216069591328	0.5216069591319	0.5216069591319
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33	Example 2					a =	1	b =	3	b-a =	2
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35	l			Odd Sum	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32
36	1	I(1,2)	1.9387474094448	1.938747409	1.082682266
37	2	I(1,4)	1.9871949017221	2.035642394	0.7530642905	1.282578103
38	3	I(1,8)	1.9988379984499	4.02096219	0.5595796814	0.9313197282	1.200563042	1.329499739
39	4	I(1,16)	2.0017211056880	8.018416852	0.4622493139	0.6572841836	0.844951075	1.010884791	1.146043307	1.246067151	1.310282402	1.340654628
40	5	I(1,32)	2.0024401836776	16.02527409	0.4145232831	0.510712112	0.6085362147	0.7055458511	0.7996039854	0.8889133043	0.9720202156	1.047802849	1.115448446	1.174424239	1.224444867	1.265438588	1.29751388	1.320927552	1.336055081	1.343363627
41	6	I(1,64)	2.0026198474936	32.04479218	0.3910440662	0.4382728909	0.4864097173	0.5351154452	0.5840658718	0.6329541063	0.6814923596	0.7294132003	0.7764703556	0.8224391258	0.8671164758	0.9103208559	0.9518918012	0.9916893493	1.029593315	1.065502449	1.099333516	1.131020305	1.160512602	1.187775135	1.212786513	1.23553816	1.256033271	1.27428578	1.290319363	1.304166468	1.315867391	1.325469382	1.333025807	1.338595341	1.342241223	1.344030542
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44				Table of I(P,2^l)
45		P
46	l	1	2	3	4	5	6
47	1	1.9387474094448
48	2	1.9871949017221	2.0033440658145
49	3	1.9988379984499	2.0027190306925	2.0026773616844
50	4	2.0017211056880	2.0026821414340	2.0026796821501	2.0026797189829
51	5	2.0024401836776	2.0026798763408	2.0026797253346	2.0026797260200	2.0026797260476
52	6	2.0026198474936	2.0026797354323	2.0026797260384	2.0026797260496	2.0026797260497	2.0026797260497
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