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This file was processed as: Mailbox/MIME Entity
(archive/mbox ).
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100%
dexvert
Mailbox/MIME Entity (archive/mbox)
magic
Supported
1%
dexvert
Swift 3D 3D Graphic (poly/swift3D3DGraphic)
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Unsupported
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Text File (text/txt)
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file
Mailbox text, 1st line "From pdxgate!qiclab!psgrain!ogicse!cs.uoregon.edu!news.uoregon.edu!cie.uoregon.edu!scavo Wed Mar 3 09:23:01 PST 1993", ASCII text
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Likely Text (Perl)
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Textdatei (UNIX)
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Format: plain text[LF]
default (weak)
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xdgMime
application/mbox
default
hex view +--------+-------------------------+-------------------------+--------+--------+ |00000000| 46 72 6f 6d 20 70 64 78 | 67 61 74 65 21 71 69 63 |From pdx|gate!qic| |00000010| 6c 61 62 21 70 73 67 72 | 61 69 6e 21 6f 67 69 63 |lab!psgr|ain!ogic| |00000020| 73 65 21 63 73 2e 75 6f | 72 65 67 6f 6e 2e 65 64 |se!cs.uo|regon.ed| |00000030| 75 21 6e 65 77 73 2e 75 | 6f 72 65 67 6f 6e 2e 65 |u!news.u|oregon.e| |00000040| 64 75 21 63 69 65 2e 75 | 6f 72 65 67 6f 6e 2e 65 |du!cie.u|oregon.e| |00000050| 64 75 21 73 63 61 76 6f | 20 57 65 64 20 4d 61 72 |du!scavo| Wed Mar| |00000060| 20 20 33 20 30 39 3a 32 | 33 3a 30 31 20 50 53 54 | 3 09:2|3:01 PST| |00000070| 20 31 39 39 33 0a 0a 49 | 6e 20 61 72 74 69 63 6c | 1993..I|n articl| |00000080| 65 20 3c 31 39 39 33 4d | 61 72 31 2e 31 37 30 36 |e <1993M|ar1.1706| |00000090| 34 38 2e 31 39 32 39 34 | 40 6d 61 74 68 2e 75 63 |48.19294|@math.uc| |000000a0| 6c 61 2e 65 64 75 3e 20 | 73 7a 68 6f 6e 67 40 6a |la.edu> |szhong@j| |000000b0| 6f 73 68 75 61 2e 6d 61 | 74 68 2e 75 63 6c 61 2e |oshua.ma|th.ucla.| |000000c0| 65 64 75 20 28 53 69 66 | 65 6e 20 5a 68 6f 6e 67 |edu (Sif|en Zhong| |000000d0| 29 20 77 72 69 74 65 73 | 3a 0a 3e 0a 3e 49 73 20 |) writes|:.>.>Is | |000000e0| 4e 65 77 74 6f 6e 27 73 | 20 6d 65 74 68 6f 64 20 |Newton's| method | |000000f0| 74 68 65 20 62 65 73 74 | 20 6d 65 74 68 6f 64 20 |the best| method | |00000100| 74 6f 20 63 6f 6d 70 75 | 74 65 20 61 20 63 75 62 |to compu|te a cub| |00000110| 69 63 20 72 6f 6f 74 3f | 0a 0a 44 65 70 65 6e 64 |ic root?|..Depend| |00000120| 73 20 6f 6e 20 77 68 61 | 74 20 79 6f 75 20 6d 65 |s on wha|t you me| |00000130| 61 6e 20 62 79 20 22 62 | 65 73 74 22 2e 20 20 4e |an by "b|est". N| |00000140| 65 77 74 6f 6e 27 73 20 | 6d 65 74 68 6f 64 20 69 |ewton's |method i| |00000150| 73 20 61 0a 71 75 61 64 | 72 61 74 69 63 61 6c 6c |s a.quad|raticall| |00000160| 79 20 63 6f 6e 76 65 72 | 67 69 6e 67 20 61 6c 67 |y conver|ging alg| |00000170| 6f 72 69 74 68 6d 2c 20 | 62 75 74 20 74 68 65 72 |orithm, |but ther| |00000180| 65 20 61 72 65 20 68 69 | 67 68 65 72 2d 0a 6f 72 |e are hi|gher-.or| |00000190| 64 65 72 20 74 65 63 68 | 6e 69 71 75 65 73 20 6c |der tech|niques l| |000001a0| 69 6b 65 2c 20 73 61 79 | 2c 20 48 61 6c 6c 65 79 |ike, say|, Halley| |000001b0| 27 73 20 6d 65 74 68 6f | 64 2e 20 20 54 68 65 20 |'s metho|d. The | |000001c0| 69 74 65 72 61 74 69 6f | 6e 0a 0a 20 20 20 20 20 |iteratio|n.. | |000001d0| 20 20 20 20 32 78 5e 33 | 20 2b 20 34 72 0a 20 20 | 2x^3| + 4r. | |000001e0| 20 78 27 20 3d 20 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d | x' = --|--------| |000001f0| 2d 20 78 0a 20 20 20 20 | 20 20 20 20 20 34 78 5e |- x. | 4x^| |00000200| 33 20 2b 20 32 72 0a 0a | 69 73 20 63 75 62 69 63 |3 + 2r..|is cubic| |00000210| 61 6c 6c 79 20 63 6f 6e | 76 65 72 67 69 6e 67 20 |ally con|verging | |00000220| 74 6f 20 74 68 65 20 63 | 75 62 65 20 72 6f 6f 74 |to the c|ube root| |00000230| 20 6f 66 20 20 72 20 2c | 20 66 6f 72 20 65 78 61 | of r ,| for exa| |00000240| 6d 70 6c 65 0a 28 69 74 | 27 73 20 67 65 6e 65 72 |mple.(it|'s gener| |00000250| 61 6c 69 7a 61 74 69 6f | 6e 20 74 6f 20 6e 74 68 |alizatio|n to nth| |00000260| 20 72 6f 6f 74 73 20 69 | 73 20 64 75 65 20 74 6f | roots i|s due to| |00000270| 20 4c 61 6d 62 65 72 74 | 20 69 6e 20 31 37 37 30 | Lambert| in 1770| |00000280| 29 2e 0a 41 6e 64 20 74 | 68 65 72 65 27 73 20 6e |)..And t|here's n| |00000290| 6f 20 65 6e 64 20 74 6f | 20 68 69 67 68 65 72 2d |o end to| higher-| |000002a0| 6f 72 64 65 72 20 69 74 | 65 72 61 74 69 76 65 20 |order it|erative | |000002b0| 6d 65 74 68 6f 64 73 20 | 73 75 63 68 20 61 73 0a |methods |such as.| |000002c0| 74 68 69 73 20 28 63 66 | 2e 20 49 2e 20 4b 69 73 |this (cf|. I. Kis| |000002d0| 73 2e 20 20 41 20 67 65 | 6e 65 72 61 6c 69 7a 61 |s. A ge|neraliza| |000002e0| 74 69 6f 6e 20 6f 66 20 | 4e 65 77 74 6f 6e 27 73 |tion of |Newton's| |000002f0| 20 61 70 70 72 6f 78 69 | 6d 61 74 69 6f 6e 0a 70 | approxi|mation.p| |00000300| 72 6f 63 65 64 75 72 65 | 20 5b 47 65 72 6d 61 6e |rocedure| [German| |00000310| 5d 2e 20 20 5f 5a 2e 20 | 61 6e 67 65 77 2e 20 4d |]. _Z. |angew. M| |00000320| 61 74 68 2e 20 4d 65 63 | 68 2e 5f 20 33 34 2c 20 |ath. Mec|h._ 34, | |00000330| 36 38 2d 2d 36 39 2c 20 | 31 39 35 34 2e 29 0a 62 |68--69, |1954.).b| |00000340| 75 74 20 6f 66 20 63 6f | 75 72 73 65 20 74 68 65 |ut of co|urse the| |00000350| 20 70 72 69 63 65 20 79 | 6f 75 20 70 61 79 20 69 | price y|ou pay i| |00000360| 73 20 6d 6f 72 65 20 63 | 6f 6d 70 75 74 61 74 69 |s more c|omputati| |00000370| 6f 6e 20 70 65 72 20 69 | 74 65 72 61 74 69 6f 6e |on per i|teration| |00000380| 2e 0a 0a 2d 2d 20 0a 54 | 6f 6d 20 53 63 61 76 6f |...-- .T|om Scavo| |00000390| 0a 73 63 61 76 6f 40 63 | 69 65 2e 75 6f 72 65 67 |.scavo@c|ie.uoreg| |000003a0| 6f 6e 2e 65 64 75 0a 0a | 0a |on.edu..|. | +--------+-------------------------+-------------------------+--------+--------+