{"id":101947,"date":"2023-11-13T16:25:38","date_gmt":"2023-11-13T16:25:38","guid":{"rendered":"https:\/\/science-hub.click\/%E3%83%8B%E3%83%A5%E3%83%BC%E3%83%88%E3%83%B3%E3%83%95%E3%83%A9%E3%82%AF%E3%82%BF%E3%83%AB%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2023-11-13T16:25:38","modified_gmt":"2023-11-13T16:25:38","slug":"%E3%83%8B%E3%83%A5%E3%83%BC%E3%83%88%E3%83%B3%E3%83%95%E3%83%A9%E3%82%AF%E3%82%BF%E3%83%AB%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=101947","title":{"rendered":"\u30cb\u30e5\u30fc\u30c8\u30f3 \u30d5\u30e9\u30af\u30bf\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"

\u5c0e\u5165<\/h2>
\n\"\"<\/figure>
\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u30d5\u30e9\u30af\u30bf\u30ebz<\/i> 3<\/sup> \u2212 1<\/span>\u3068\u591a\u9805\u5f0f\u306e\u6839\u306e\u5f15\u529b\u306e 3 \u3064\u306e\u76c6\u5730 (\u30ab\u30e9\u30fc)<\/div><\/div><\/div>

\u300c\u30cb\u30e5\u30fc\u30c8\u30f3 \u30d5\u30e9\u30af\u30bf\u30eb\u300d\u306f\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u3092\u591a\u9805\u5f0f<\/a><\/span>\u306b\u9069\u7528\u3059\u308b\u3053\u3068\u3092\u7279\u5fb4\u3068\u3059\u308b\u8907\u7d20\u5e73\u9762<\/a><\/span>\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u5883\u754c<\/a><\/span>\u30bb\u30c3\u30c8\u3067\u3059\u3002

$$ {\\textstyle{p(z), z\\in\\mathbb{C}}} $$<\/div> \u3002<\/p>

\u610f\u5473<\/h2>

\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u30d5\u30e9\u30af\u30bf\u30eb<\/a><\/span>\u306f\u6709\u7406\u578b\u95a2\u6570\u306e\u30b8\u30e5\u30ea\u30a2\u96c6\u5408\u3067\u3059

$$ {z\\mapsto z-\\frac{p(z)}{p'(z)}} $$<\/div>\u3053\u308c\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u3067\u6c42\u3081\u3089\u308c\u307e\u3059\u3002\u9b45\u529b\u7684\u306a\u30b5\u30a4\u30af\u30eb\u304c\u306a\u3044\u5834\u5408\u3001\u8907\u7d20\u5e73\u9762\u3092\u9818\u57dfG<\/i> k<\/i><\/sub><\/span>\u306b\u5206\u5272\u3057\u3001\u305d\u308c\u305e\u308c\u306e\u9818\u57df\u304c\u3053\u306e\u591a\u9805\u5f0f\u306e\u5404\u6839\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u307e\u3059\u3002<\/p>

\u3057\u305f\u304c\u3063\u3066\u3001\u53e4\u5178\u7684\u306a\u30cb\u30e5\u30fc\u30c8\u30f3 \u30d5\u30e9\u30af\u30bf\u30eb\u306f<\/b>\u591a\u9805\u5f0fz<\/i> 3<\/sup> \u2212 1<\/span><\/b>\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u3001\u5e73\u9762\u3092\u305d\u306e 3 \u3064\u306e\u6839\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u305f 3 \u3064\u306e\u9818\u57df\u306b\u5206\u5272\u3057\u307e\u3059\u3002

$$ {\\scriptstyle{1, -1\/2+\\frac{\\sqrt{3}}{2}i}} $$<\/div>\u305d\u3057\u3066
$$ {\\scriptstyle{-1\/2-\\frac{\\sqrt{3}}{2}i}} $$<\/div> \u3002<\/p>

\u5de5\u4e8b<\/span><\/h3>

\u8907\u7d20\u5e73\u9762\u306e\u591a\u304f\u306e\u70b9\u306f\u3001\u6b21\u306e\u65b9\u6cd5\u3067\u5404\u30eb\u30fc\u30c8\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u307e\u3059\u3002<\/p>

\u8907\u7d20\u5e73\u9762\u306e\u70b9<\/a><\/span>z<\/i> 0<\/sub><\/span>\u304c\u958b\u59cb\u70b9\u3068\u3057\u3066\u9078\u629e\u3055\u308c\u307e\u3059\u3002\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u53cd\u5fa9\u6cd5\u3092\u9069\u7528\u3057\u307e\u3059\u3002<\/p>

\u7279\u306b\u3001\u53e4\u5178\u7684\u306a\u30cb\u30e5\u30fc\u30c8\u30f3 \u30d5\u30e9\u30af\u30bf\u30eb\u306f\u3001\u4ee5\u4e0b\u3092\u53cd\u5fa9\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u53d6\u5f97\u3055\u308c\u307e\u3059\u3002

$$ {\\textstyle{z_{n+1}=z_n-\\frac{z_n^3-1}{3z_n^2}=\\frac{2z_n^3+1}{3z_n^2}}} $$<\/div><\/p>

\u3053\u306e\u898f\u5247\u306b\u3088\u308a\u3001\u70b9z<\/i> 1<\/sub><\/span> \u3001 z<\/i> 2<\/sub><\/span>\u306a\u3069\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u5f97\u3089\u308c\u307e\u3059<\/a><\/span>\u3002\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u591a\u9805\u5f0f\u306e\u6839R<\/i> k<\/i><\/sub><\/span>\u306b\u5411\u304b\u3063\u3066\u53ce\u675f\u3059\u308b\u5834\u5408\u3001 z<\/i> 0 \u306f<\/sub><\/span>\u9818\u57dfG<\/i> k<\/i><\/sub><\/span>\u306b\u5c5e\u3057\u307e\u3059\u3002\u3053\u306e\u9818\u57df\u306f\u300c\u6839\u306e\u5f15\u529b\u76c6\u5730R<\/i> k<\/i><\/sub><\/span> \u300d\u3068\u3082\u547c\u3070\u308c\u307e\u3059\u3002<\/p>

\u305f\u3060\u3057\u3001\u5c11\u306a\u304f\u3068\u3082 2\u6b21<\/span>\u306e\u591a\u9805\u5f0f<\/a><\/span>\u3067\u306f\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u6570\u5217\u304c\u53ce\u675f\u3057\u306a\u3044\u70b9\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u5404\u6839\u306e\u5f15\u529b\u9818\u57df\u306e\u5883\u754c\u306e\u5834\u5408\u3067\u3059\u3002<\/p>

\u30d5\u30e9\u30af\u30bf\u30eb\u69cb\u9020<\/span><\/h3>

\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u30d5\u30e9\u30af\u30bf\u30eb\u306f\u3001\u4ed6\u306e\u30d5\u30e9\u30af\u30bf\u30eb\u3068\u540c\u69d8\u306b\u3001\u5358\u7d14\u306a\u8aac\u660e\u306b\u3082\u95a2\u308f\u3089\u305a\u8907\u96d1\u306a\u5916\u89b3\u3092\u793a\u3057\u3001\u3042\u3089\u3086\u308b\u30b9\u30b1\u30fc\u30eb\u3067\u898b\u3089\u308c\u308b\u81ea\u5df1\u76f8\u4f3c\u6027\u3092\u793a\u3057\u307e\u3059 (\u4ee5\u4e0b\u306e\u9023\u7d9a\u30ba\u30fc\u30e0\u3092\u53c2\u7167)\u3002<\/p>

\u30cb\u30e5\u30fc\u30c8\u30f3z<\/i> 3<\/sup> \u2212 1<\/span><\/p><\/div><\/div><\/td>

\u7b2c1\u30ba\u30fc\u30e0<\/p><\/div><\/div><\/td>

2\u756a\u76ee\u306e\u30ba\u30fc\u30e0<\/p><\/div><\/div><\/td><\/tr><\/table>

\u307e\u305f\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u306f\u521d\u671f\u6761\u4ef6\u306b\u975e\u5e38\u306b\u654f\u611f\u3067\u3042\u308a\u3001\u7121\u9650\u306b\u8fd1\u3044 2 \u3064\u306e\u521d\u671f\u70b9\u304c\u7570\u306a\u308b\u6839\u306b\u53ce\u675f\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u3082\u793a\u5506\u3057\u3066\u3044\u307e\u3059\u3002<\/p>

\u6700\u5f8c\u306b\u3001\u30cb\u30e5\u30fc\u30c8\u30f3 \u30d5\u30e9\u30af\u30bf\u30eb\u306e\u5404\u70b9\u304c\u3001n \u500b\u306e\u5f15\u529b\u9818\u57df\u306e\u305d\u308c\u305e\u308c\u3092\u5206\u96e2\u3059\u308b\u8907\u6570\u306e\u5883\u754c\u70b9\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002 2 \u3064\u306e\u7121\u9650\u306b\u8fd1\u3044\u70b9\u304c 2 \u3064\u306e\u7570\u306a\u308b\u30eb\u30fc\u30c8\u306b\u53ce\u675f\u3059\u308b<\/span>\u5834\u5408\u3001\u540c\u69d8\u306b\u7121\u9650\u306b\u8fd1\u3044 3 \u756a\u76ee\u306e\u30eb\u30fc\u30c8\u306b\u53ce\u675f\u3059\u308b 3 \u756a\u76ee\u306e\u70b9\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u548c\u7530\u6e56\u306b\u3064\u3044\u3066\u306f\u3053\u3061\u3089\u306e\u8a18\u4e8b\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>

\u4e00\u822c\u5316<\/a><\/span><\/span><\/h3>

\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u53cd\u5fa9\u3092\u4e00\u822c\u5316\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {z_{n+1}=z_n- a \\frac{p(z_n)}{p'(z_n)} } $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001 a \u306f<\/i><\/span>\u8907\u7d20\u6570<\/a><\/span>\u3067\u3059\u3002\u7279\u6b8a\u306a\u30b1\u30fc\u30b9a<\/i> = 1<\/span>\u306f\u3001\u53e4\u5178\u7684\u306a\u30cb\u30e5\u30fc\u30c8\u30f3 \u30d5\u30e9\u30af\u30bf\u30eb\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002a\u304c<\/i><\/span>\u534a\u5f84 1 \u306e 1 \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u5186\u76e4<\/span>\u306b\u5c5e\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u3053\u306e\u5909\u63db\u306e\u4e0d\u52d5\u70b9\u306f\u5b89\u5b9a\u3057\u307e\u3059\u3002\u3053\u306e\u5186\u76e4\u306e\u5916\u5074\u3067\u306f\u3001\u56fa\u5b9a\u70b9\u306f\u5c40\u6240\u7684\u306b\u4e0d\u5b89\u5b9a\u3067\u3059\u304c\u3001\u5909\u63db\u306f\u30b8\u30e5\u30ea\u30a2\u96c6\u5408<\/a><\/span>\u306e\u610f\u5473<\/a><\/span>\u3067\u30d5\u30e9\u30af\u30bf\u30eb\u69cb\u9020\u3092\u793a\u3057\u307e\u3059\u3002 p \u304c<\/i><\/span>\u6b21\u6570n<\/i><\/span>\u306e\u591a\u9805\u5f0f\u306e\u5834\u5408\u3001\u30b7\u30fc\u30b1\u30f3\u30b9z<\/i> n \u306f\u3001<\/i><\/sub><\/span> a \u304c<\/i><\/span>n \u3092<\/i><\/span>\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84n<\/i><\/span>\u306e\u5186\u76e4\u5185\u306b\u7559\u307e\u308b\u9650\u308a\u3001\u6709\u754c\u3068\u306a\u308a\u307e\u3059\u3002<\/p>

\u305d\u306e\u4ed6\u306e\u65b9\u6cd5<\/span><\/h3>

\u6570\u5024<\/span>\u89e3\u6790\u3067\u306f\u3001\u591a\u6570<\/a><\/span>\u306e\u65b9\u7a0b\u5f0f<\/a><\/span>\u89e3\u6c7a\u65b9\u6cd5\u304c\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>

\u95a2\u9023\u3059\u308b\u30d5\u30e9\u30af\u30bf\u30eb\u306f\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u30d5\u30e9\u30af\u30bf\u30eb\u3068\u5171\u901a\u306e\u7279\u5fb4\u3001\u3064\u307e\u308a\u4e09\u91cd\u5883\u754c\u3001\u3059\u3079\u3066\u306e\u30b9\u30b1\u30fc\u30eb\u3067\u306e\u81ea\u5df1\u76f8\u4f3c\u6027\u3001\u304a\u3088\u3073 3 \u3064\u306e\u7121\u95a2\u4fc2\u306a\u5f15\u529b\u76c6\u5730 (\u6d41\u308c) \u3092\u5171\u6709\u3057\u307e\u3059\u3002\u9078\u629e\u3057\u305f\u521d\u671f\u6761\u4ef6\u306b\u5fdc\u3058\u3066\u3001\u30bb\u30ab\u30f3\u30c8\u6cd5\u306f\u975e\u53ce\u675f\u30be\u30fc\u30f3\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002<\/p>

\u591a\u9805\u5f0f\u95a2\u6570z<\/i> 3<\/sup> \u2212 1<\/span>\u306b\u9069\u7528\u3055\u308c\u305f\u4ee5\u4e0b\u306e\u4f8b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>
\u65b9\u6cd5<\/th>\u5f0f<\/th>\u53ce\u675f<\/span><\/th>\u56f3<\/th>\u5099\u8003<\/th><\/tr>
\u30bb\u30ab\u30f3\u30c8\u6cd5<\/td>
$$ {\\scriptstyle{z_{n+1} = z_n – \\frac{z_n-z_{n-1}}{p(z_n)-p(z_{n-1})} p(z_n). }} $$<\/div><\/td>
 1,618<\/td>
\n\"\u6b63\u5272\u30d5\u30e9\u30af\u30bf\u30eb.jpg\"<\/figure><\/td>
\u30bb\u30ab\u30f3\u30c8\u6cd5\u3067\u306f\u3001\u5c0e\u95a2\u6570p<\/i> ‘( z<\/i> n<\/i><\/sub> ) \u3092<\/span>\u6b21\u306e\u3088\u3046\u306b\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u3067\u3001\u5c0e\u95a2\u6570<\/a><\/span>\u306e\u8a08\u7b97\u3092\u56de\u907f\u3067\u304d\u307e\u3059\u3002
$$ {\\textstyle{\\frac{p(z_n)-p(z_{n-1})}{z_n-z_{n-1}}}} $$<\/div> \u3002

\u3053\u306e\u56f3\u3067\u306f\u3001 z<\/i> \u2212 1 \u3092<\/sub><\/span>z<\/i> 0<\/sub><\/span>\u306e\u8fd1\u304f\u306b\u914d\u7f6e\u3057\u3066\u3044\u307e\u3059\u3002<\/p><\/td><\/tr>

\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5<\/td>
$$ {\\scriptstyle{z_{n+1} = z_n – \\frac{p(z_n)}{p'(z_n)}}} $$<\/div><\/td>
\u4e8c\u6b21\u95a2\u6570<\/td>
\n\"\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u30d5\u30e9\u30af\u30bf\u30eb.jpg\"<\/figure><\/td><\/tr>
\u4e16\u5e2f\u4e3b\u65b9\u5f0f<\/td>
$$ {\\scriptstyle{z_{n+1} = z_n – \\frac{p(z_n)}{p'(z_n)}\\times (1+h_n)}} $$<\/div>\u3068
$$ {\\scriptstyle{h_n = \\frac{p(z_n) p”(z_n)}{2 p'(z_n)^2}}} $$<\/div><\/td>
\u30ad\u30e5\u30fc\u30d3\u30c3\u30af<\/td>
\n\"\u30cf\u30a6\u30b9\u30db\u30eb\u30c0\u30fc\u6cd5\u30d5\u30e9\u30af\u30bf\u30eb.jpg\"<\/figure><\/td>
\u30cf\u30a6\u30b9\u30db\u30eb\u30c0\u30fc\u306e\u65b9\u6cd5\u306f\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u3068\u30cf\u30ec\u30fc\u306e\u65b9\u6cd5\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3067\u3059\u3002<\/td><\/tr>
\u30cf\u30ec\u30fc\u6cd5<\/td>
$$ {\\scriptstyle{z_{n+1} = z_n – \\frac {2 p(z_n) z'(z_n)} {2 {[z'(z_n)]}^2 – p(z_n) p”(z_n)}} } $$<\/div><\/td>
\u30ad\u30e5\u30fc\u30d3\u30c3\u30af<\/td>
\n\"\u30cf\u30ec\u30fc\u6cd5\u30d5\u30e9\u30af\u30bf\u30eb.jpg\"<\/figure><\/td><\/tr><\/table><\/div>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. \u0643\u0633\u064a\u0631\u064a\u0629 \u0646\u064a\u0648\u062a\u0646 \u2013 arabe<\/a><\/li>
  2. \u041d\u044e\u0442\u043e\u043d\u043e\u0432 \u0444\u0440\u0430\u043a\u0442\u0430\u043b \u2013 bulgare<\/a><\/li>
  3. Frakt\u00e1l Newton \u2013 tch\u00e8que<\/a><\/li>
  4. Newtonfraktal \u2013 allemand<\/a><\/li>
  5. \u03a6\u03c1\u03ac\u03ba\u03c4\u03b1\u03bb \u03c4\u03bf\u03c5 \u039d\u03b5\u03cd\u03c4\u03c9\u03bd\u03b1 \u2013 grec<\/a><\/li>
  6. Newton fractal \u2013 anglais<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u30cb\u30e5\u30fc\u30c8\u30f3 \u30d5\u30e9\u30af\u30bf\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n