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gold2007

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hank612

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Edstrayer: ÊýѧEPI+1, Ó¦ÖúÖ¸Êý+1, thank 2016-05-19 07:36:48
iάÊý: ½ð±Ò+5, ¡ï¡ï¡ï¡ï¡ï×î¼Ñ´ð°¸ 2016-05-19 17:52:19
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(1) ¿¼ÂÇ´ÎÊýСÓÚnµÄËùÓÐʵϵÊý¶àÏîʽ×é³ÉµÄnάÏßÐÔ¿Õ¼äV,¶¨ÒåÄÚ»ýΪ .  VÖÐËùÓÐϵÊýºÍΪÁãµÄ¶àÏîʽ×é³É(n-1)ά×Ó¿Õ¼äW.ÓÚÊÇWÔÚVÖеÄÕý½»²¹¿Õ¼äÄÚÓÐÇÒ½öÓÐÒ»¸ö¶àÏîʽÂú×ãf(1)=1.  
(2)ÈÝÒ׿´³ö, ÔÚVÖÐËùÓÐÂú×ãF(1)=1µÄ¶àÏîʽF(x)ÖÐ, ±ØÓÐ . Ô­ÒòºÜ¼òµ¥, ÓÉÓÚF(x)-f(x)ÊôÓÚW, ËùÒÔ, ÓÚÊÇ, ´Ó¶øfÊÇʹµÃƽ·½µÄ»ý·ÖÈ¡µ½×îСֵµ«ÏµÊýºÍÈÔΪ1µÄΨһ¶àÏîʽ.

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, ÉèÕâÒ»´®µÈʽµÄֵΪA.

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(5)ÏÖÔÚÎÒÃÇÒª²ÈÒ»²È¾ÞÈ˵ļç°òÁË.
https://en.wikipedia.org/wiki/Hilbert_matrix
µÄϵÊý¾ØÕóÇ¡ºÃÊÇHilbert matrix H, , ÓÚÊÇ
Ç¡ºÃÊÇδ֪µÄ³£ÊýA³ËÒÔ inverse Hilbert matrixµÄËùÓÐϵÊýÖ®ºÍ.
ºóÕßÈÃÎÒÃÇÔÙ²ÈSamuel Schechter»òÕß R.B.SmithµÄ¼ç°ò(ÎÄÕÂÖеÚ75Ò³µÚÒ»,¶þÐÐformula(13) )
https://math.berkeley.edu/~strai ... y.matrices.1959.pdf
È«²¿ÏµÊýºÍµÈÓÚs=n(p+n), ÕâÀïp=0, ÓÚÊÇ , µÃµ½@ iάÊý µÄ²ÂÏë
ÎÄÕÂÀïformula(16)»òÉÏÃæµÄwikipediaÁ¬½ÓÓÐHilbertÄæ¾ØÕóµÄÿ¸öÔªËØµÄ¾ßÌå±í´ïʽ,´ó¼Ò¿ÉÒԵõ½b_iµÄ¾ßÌå±í´ïʽ. ´óÖÂÊÇ ,
ÒÔ¼° ¶¼ÊÇ×ÔÈ»Êý.

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  • ¸½¼þ 1 : schechter.cauchy.matrices.1959.pdf
  • 2016-05-18 05:05:37, 388.82 K
We_must_know. We_will_know.
13Â¥2016-05-18 05:05:40
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iάÊý

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13Â¥: Originally posted by hank612 at 2016-05-18 05:05:40
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