{"id":57608,"date":"2014-09-26T02:33:17","date_gmt":"2014-09-25T18:33:17","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=57608"},"modified":"2021-10-06T16:13:30","modified_gmt":"2021-10-06T08:13:30","slug":"%e7%89%9b%e9%a0%93%e6%8f%92%e5%80%bc%e5%a4%9a%e9%a0%85%e5%bc%8f2%ef%bc%88newton-interpolating-polynomial2%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e7%89%9b%e9%a0%93%e6%8f%92%e5%80%bc%e5%a4%9a%e9%a0%85%e5%bc%8f2%ef%bc%88newton-interpolating-polynomial2%ef%bc%89\/","title":{"rendered":"\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f (2)"},"content":{"rendered":"<div class=\"pf-content\"><p><span style=\"color: #ff6600;\"><strong>\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f (2)\u00a0(Newton Interpolating polynomial)<\/strong><\/span><br \/>\n<span style=\"color: #008000;\"><strong>\u81fa\u5317\u5e02\u7acb\u7b2c\u4e00\u5973\u5b50\u9ad8\u7d1a\u4e2d\u5b78\u8607\u4fca\u9d3b\u8001\u5e2b<\/strong><\/span><\/p>\n<p>\u9023\u7d50\uff1a<a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=57609\">\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f(1)<\/a><\/p>\n<p>\u4e00\u6a23\u5f9e\u9019\u500b\u554f\u984c\u958b\u59cb<\/p>\n<p style=\"padding-left: 60px;\">\u7d66\u5b9a\u5e73\u9762\u4e0a\u4e09\u9ede \\(A(1,7)\\)\uff0c\\(B(2,6)\\)\u00a0\uff0c\\(C(3,11)\\)\uff0c\u6c42\u5716\u5f62\u901a\u904e\u9019\u4e09\u9ede\u7684\u4e8c\u6b21\u591a\u9805\u5f0f\u3002<\/p>\n<p>\u6211\u5011\u77e5\u9053\u57fa\u65bc\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f\uff0c\u53ef\u4ee5\u5047\u8a2d\u6240\u6c42\u51fd\u6578 \\(f(x)\\)\u70ba<\/p>\n<p style=\"text-align: center;\">\\(f(x) = f(1) + a(x &#8211; 1) + b(x &#8211; 1)(x &#8211; 2)\\)<\/p>\n<p>\u901a\u5e38\u958b\u982d\u9019\u500b\u5f62\u5f0f\u5c31\u662f\u521d\u5b78\u8005\u4e9f\u9700\u8de8\u8d8a\u7684\u9580\u6abb\u3002\u672c\u6587\u8a66\u5716\u5229\u7528\u5b78\u751f\u5df2\u7d93\u64c1\u6709\u7684\u591a\u9805\u5f0f\u77e5\u8b58\uff0c\u63d0\u4f9b\u4e00\u500b\u6559\u5b78\u4e0a\u53ef\u884c\u7684\u5f15\u5c0e\uff0c\u5c1a\u8acb\u65b9\u5bb6\u4e0d\u541d\u6307\u6559\u3002\u81f3\u65bc\u5b78\u751f\u9700\u8981\u77e5\u9053\u4ec0\u9ebc\u591a\u9805\u5f0f\u7684\u77e5\u8b58\u5462\uff1f\u53ea\u8981\u56e0\u5f0f\u5b9a\u7406\u5373\u53ef\u3002<\/p>\n<p><!--more--><\/p>\n<p>\u8907\u7fd2\u4e00\u4e0b \u00a0\u00a0<strong>\u56e0\u5f0f\u5b9a\u7406<\/strong><\/p>\n<p style=\"padding-left: 60px;\">\u8a2d \\(f(x)\\)\u00a0\u70ba\u591a\u9805\u5f0f\uff0c\\(ax-b\\)\u00a0\u70ba\u4e00\u6b21\u591a\u9805\u5f0f\u3002<\/p>\n<p style=\"padding-left: 60px;\">\\(f\\left( {\\frac{b}{a}} \\right) = 0 \\Leftrightarrow\\) \u662f \\(f(x)\\)\u00a0\u7684\u56e0\u5f0f\u3002<\/p>\n<p>\u7c21\u8a00\u4e4b\uff0c\u53ea\u8981\u6709\u4e00\u6b21\u56e0\u5f0f\uff0c\u5c31\u8868\u793a\u591a\u9805\u5f0f\u7684\u503c\u70ba \\(0\\)\u3002\u4f8b\u5982\uff0c\u591a\u9805\u5f0f \\(f(x)\\)\u00a0\u6709\u4e00\u6b21\u56e0\u5f0f \\(x+2\\)\uff0c\u4ee3\u8868 \\(f(-2)=0\\)\u3002\u53cd\u4e4b\uff0c\u82e5\u591a\u9805\u5f0f \\(f(x)\\)\u00a0\u6eff\u8db3 \\(f(1)=0\\)\uff0c\u4ee3\u8868 \\(f(x)\\)\u00a0\u6709 \\(x-1\\)\u00a0\u7684\u56e0\u5f0f\u3002<\/p>\n<p>\u9032\u4e00\u6b65\u63a8\u5ee3\uff0c\u6613\u77e5\u4e0b\u9762\u9019\u500b\u91cd\u8981\u7684\u6027\u8cea\uff1a<\/p>\n<p style=\"padding-left: 60px;\">\u82e5 \\(a_1,a_2,\\cdots,a_n\\)\u00a0\u662f \\(n\\)\u00a0\u500b\u4e0d\u540c\u7684\u5be6\u6578\uff0c<br \/>\n\u4e14\u591a\u9805\u5f0f \\(f(x)\\)\u00a0\u6eff\u8db3 \\(f\\left( {{a_1}} \\right) = f\\left( {{a_2}} \\right) =\\cdots= f\\left( {{a_n}} \\right) = 0\\)\uff0c<br \/>\n\u5247\u00a0\\(\\left( {x &#8211; {a_1}} \\right)\\left( {x &#8211; {a_2}} \\right) \\cdots \\left( {x &#8211; {a_n}} \\right)\\)\u00a0\u662f \\(f(x)\\)\u00a0\u7684\u56e0\u5f0f\u3002<\/p>\n<p>\u73fe\u5728\u8b93\u6211\u5011\u56de\u5230\u958b\u59cb\u7684\u554f\u984c\u4e0a\u3002\u986f\u7136\u5716\u5f62\u904e\u9019\u4e09\u9ede\u7684\u4e8c\u6b21\u51fd\u6578 \\(f(x)\\)\u00a0\u6eff\u8db3 \\(f(1)=7,f(2)=6,f(3)=11\\)\u3002\u5982\u4f55\u6c42\u9019\u6a23\u7684\u4e8c\u6b21\u51fd\u6578 \\(f(x)\\)\u00a0\u5462\uff1f\u96d6\u7136\uff0c\u6211\u5011\u53ef\u4ee5\u8a2d \\(f(x)=ax^2+bx+c\\)\uff0c\u5c07\u4e09\u500b\u689d\u4ef6\u4ee3\u5165\u6c42\u5f97 \\(a,b,c\\)\u3002\u4f46\u9019\u4e0d\u662f\u6211\u5011\u7684\u76ee\u6a19\u3002<\/p>\n<p>\u4e0d\u904e\uff0c\u9019\u537b\u8b93\u6211\u5011\u77e5\u9053\uff1a\u4e00\u822c\u800c\u8a00\uff0c\u5df2\u77e5\u4e09\u9ede\uff0c\u80fd\u6c42\u7684\u662f\u4e8c\u6b21\u591a\u9805\u5f0f\uff1b\u66f4\u4e00\u822c\u800c\u8a00\uff0c\u77e5\u9053 \\(n+1\\)\u00a0\u500b\u9ede\uff0c\u80fd\u6c42\u7684\u6700\u4f4e\u6b21\u6578\u7684\u591a\u9805\u5f0f\u70ba \\(n\\)\u00a0\u6b21\u591a\u9805\u5f0f\u3002<\/p>\n<p>\u6211\u5011\u63db\u500b\u89d2\u5ea6\u4f86\u8003\u616e\u4e0a\u9762\u7684\u554f\u984c\uff0c\u82e5\u53ea\u8003\u616e\u4e00\u500b\u9ede\u5462\uff1f\u4f8b\u5982\uff0c\u9ede \\(A(1,7)\\)\u3002\u90a3\u9ebc\uff0c\u6eff\u8db3\u7684\u591a\u9805\u5f0f\u51fd\u6578 \\(f_1(x)\\)\u00a0\u662f\u4ec0\u9ebc\uff1f\u9996\u5148\uff0c\\(f_1(x)\\) \u61c9\u8a72\u662f\u96f6\u6b21\u591a\u9805\u5f0f\uff0c\u4e5f\u5c31\u662f\u5e38\u6578\u591a\u9805\u5f0f\u3002\u56e0\u6b64\uff0c\u4e0d\u96e3\u731c\u51fa\u7d50\u679c\uff1a\\(f_1(x)=7\\)\u3002<\/p>\n<p>\u63a5\u4e0b\u4f86\uff0c\u82e5\u518d\u589e\u52a0\u4e00\u500b\u9ede\u5462\uff1f\u9ede \\(B(2,6)\\)\u3002\u70ba\u4e86\u548c\u524d\u9762\u7684\u51fd\u6578\u5340\u5225\uff0c\u6211\u5011\u7a31\u540c\u6642\u6eff\u8db3\u9ede\u00a0\\(A(1,7)\\)\u00a0\u548c\u9ede\u00a0\\(B(2,6)\\)\u00a0\u7684\u591a\u9805\u5f0f\u51fd\u6578\u70ba \\(f_2(x)\\)\u3002\u90a3\u9ebc\u00a0\\(f_2(x)\\)\uff0c\u61c9\u8a72\u662f\u4e00\u6b21\u51fd\u6578\u5427\uff01\u4e26\u4e14\uff0c\u5b83\u6eff\u8db3 \\(f_2(1)=7=f_1(1)\\)\u00a0\u8207 \\(f_2(2)=6\\)\u3002<\/p>\n<p>\u5982\u6b64\u4e00\u4f86\uff0c\\(f_2(x)\\)\u00a0\u6703\u662f\u4ec0\u9ebc\u6a23\u5b50\u5462\uff1f\u9996\u5148\uff0c\\(f_2(1)=7=f_1(1)\\)\uff0c\u4e14 \\(f_1(x)=7\\)\u00a0\u662f\u96f6\u6b21\u591a\u9805\u5f0f\uff0c\u6211\u5011\u53ef\u4ee5\u5408\u7406\u731c\u6e2c \\(f_2(x)=f_1(x)+Q_1(x)\\)\uff0c\u5176\u4e2d \\(Q_1(x)\\) \u5fc5\u70ba\u4e00\u6b21\u591a\u9805\u5f0f\uff0c\u4e14\u6eff\u8db3 \\(Q_1(1)=0\\)\uff0c\u624d\u80fd\u7b26\u5408\u00a0\\({f_2}(1) = {f_1}(1) + {Q_1}(1) = 7 + 0 = 7\\)\u00a0\u7684\u689d\u4ef6\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u7531\u56e0\u5f0f\u5b9a\u7406\u77e5\uff0c\u53ef\u4ee4<\/p>\n<p style=\"padding-left: 60px;\">\\({Q_1}(x) = a(x &#8211; 1) \\Rightarrow {f_2}(x) = {f_1}(x) + {Q_1}(x) = 7 + a(x &#8211; 1)\\)<\/p>\n<p>\u5c07 \\(f_2(2)=6\\)\u00a0\u4ee3\u5165\uff0c\u5f97 \\(7+a(2-1)=6\\Rightarrow a=-1\\)\u3002\u6240\u4ee5\uff0c\u6eff\u8db3 \\(f_2(1)=7\\)\u00a0\u8207\u00a0\\(f_2(2)=6\\) \u7684\u4e00\u6b21\u51fd\u6578\u70ba \\({f_2}(x) = {f_1}(x) &#8211; (x &#8211; 1) = 7 &#8211; (x &#8211; 1)\\)\u3002<\/p>\n<p>\u7e7c\u7e8c\u76f8\u540c\u7684\u7a0b\u5e8f\uff0c\u518d\u589e\u52a0\u9ede \\(C(3,11)\\)\uff0c\u90a3\u9ebc\uff0c\u540c\u6642\u6eff\u8db3\u9019\u4e09\u500b\u9ede\u7684\u51fd\u6578 \\(f_3(x)\\)\u00a0\u5982\u4f55\u6c7a\u5b9a\u5462\uff1f<\/p>\n<p>\u540c\u6a23\u5730\uff0c\u6211\u5011\u53ef\u4ee5\u77e5\u9053 \\(f_3(x)\\)\u00a0\u61c9\u7576\u662f\u4e8c\u6b21\u591a\u9805\u5f0f\u51fd\u6578\u3002\u540c\u6642\uff0c\u5b83\u4e5f\u6eff\u8db3\u00a0\\({f_3}(1) = {f_2}(1) = 7\\)\uff0c\\({f_3}(2) = {f_2}(2) = 6\\)\uff0c\u4ee5\u53ca \\(f_3(3)=11\\)\u3002\u56e0\u6b64\uff0c\\({f_3}(x) = {f_2}(x) + {Q_2}(x)\\)\uff0c\u5176\u4e2d \\(Q_2(x)\\)\u00a0\u5fc5\u70ba\u4e8c\u6b21\u591a\u9805\u5f0f\uff0c\u4e14\u6eff\u8db3 \\(Q_2(1)=Q_2(2)=0\\)\u3002<\/p>\n<p>\u7531\u56e0\u5f0f\u5b9a\u7406\u7684\u63a8\u5ee3\u6027\u8cea\uff0c\u53ef\u4ee4 \\(Q_2(x)=b(x-1)(x-2)\\)\uff0c<\/p>\n<p>\u5247 \\({f_3}(x) = {f_2}(x) + {Q_2}(x) = 7 &#8211; (x &#8211; 1) + b(x &#8211; 1)(x &#8211; 2)\\)<\/p>\n<p>\u5c07 \\(f_3(3)=11\\)\u00a0\u4ee3\u5165\uff0c\u5f97 \\(11=7-(3-1)+b(3-1)(3-2)\\Rightarrow b=3\\)\uff0c<\/p>\n<p>\u56e0\u6b64\uff0c\u6eff\u8db3 \\(f_3(1)=7\\)\uff0c\\(f_3(2)=6\\)\uff0c\u548c\u00a0\\(f_3(3)=11\\)\u00a0\u7684\u4e8c\u6b21\u51fd\u6578 \\(f_3(x)\\)\u00a0(\u4e5f\u662f\u6587\u7ae0\u958b\u982d\u554f\u984c\u6240\u6c42\u7684\u51fd\u6578 \\(f(x)\\))\u70ba\u00a0\\(f(x) = {f_3}(x) = 7 &#8211; (x &#8211; 1) + 3(x &#8211; 1)(x &#8211; 2)\\)<\/p>\n<p>\u89c0\u5bdf\u4e0a\u5f0f\uff0c\u4e0d\u96e3\u767c\u73fe \\(f(x)\\)\u00a0\u7531\u4e09\u500b\u55ae\u9805\u76f8\u52a0\u800c\u6210 \\(f(x)=f_1(x)+Q_1(x)+Q_2(x)\\)\uff0c<br \/>\n\u5176\u4e2d \\(f_1(1)=7,Q_1(1)=0,Q_2(1)=Q_2(2)=0\\)\u3002<\/p>\n<p>\u56de\u9867\u6574\u500b\u5c0b\u627e \\(f(x)\\)\u00a0\u7684\u904e\u7a0b\uff1a<\/p>\n<p>\u9010\u4e00\u52a0\u5165\u689d\u4ef6\u7d0d\u5165\u8003\u616e\uff0c\u5148\u662f \\(f(1)=7\\)\uff0c\u63a5\u8457\u00a0\\(\\left\\{ \\begin{array}{l} f(1) = 7\\\\ f(2) = 6 \\end{array} \\right.\\)\uff0c\u518d\u4f86 \\(\\left\\{ \\begin{array}{l} f(1) = 7\\\\ f(2) = 6\\\\ f(3) = 11 \\end{array} \\right.\\)\u3002<\/p>\n<p>\u589e\u52a0\u689d\u4ef6\u7684\u7d50\u679c\uff0c\u591a\u9805\u5f0f\u6b21\u6578\u6703\u63d0\u9ad8\uff0c\u6240\u4ee5\u6dfb\u52a0\u55ae\u9805\u662f\u5fc5\u8981\u7684\u3002\u4f46\u53c8\u8981\u4fdd\u6301\u539f\u689d\u4ef6\u6210\u7acb\uff0c<\/p>\n<p>\u6dfb\u52a0\u7684\u6bcf\u500b\u55ae\u9805\u5fc5\u9808\u4e0d\u5f71\u97ff\u539f\u6709\u689d\u4ef6\uff1a<br \/>\n\\(\\left\\{ \\begin{array}{l} f(1) = 7 \\leftrightarrow {Q_1}(1) = 0\\\\ f(2) = 6 \\end{array} \\right.\\)\uff1b\\(\\left\\{ \\begin{array}{l} f(1) = 7 \\leftrightarrow {Q_2}(1) = 0\\\\ f(2) = 6 \\leftrightarrow {Q_2}(2) = 0\\\\ f(3) = 11 \\end{array} \\right.\\)\u3002<\/p>\n<p>\u7531\u56e0\u5f0f\u5b9a\u7406\uff0c\\({Q_1}(x) = a(x &#8211; 1)\\)\u00a0\uff0c\\({Q_2}(x) = b(x &#8211; 1)(x &#8211; 2)\\)\u00a0\u81ea\u7136\u5c31\u51fa\u73fe\uff0c\u800c\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f\u7684\u5f62\u5f0f\u4e5f\u5c31\u5e95\u5b9a\u3002\u6b64\u5916\uff0c\u7531\u4e0a\u8ff0\u8aaa\u660e\u4e5f\u4e0d\u96e3\u767c\u73fe\uff0c\u96a8\u8457\u6211\u5011\u8003\u616e\u52a0\u5165\u689d\u4ef6\u7684\u6b21\u5e8f\u4e0d\u540c\uff0c\u5047\u8a2d\u7684\u591a\u9805\u5f0f\u51fd\u6578\u4e5f\u6703\u4e0d\u540c\u3002\u4f8b\u5982\uff0c\u82e5\u662f \\(f(3) = 11 \\to f(2) = 6 \\to f(1) = 7\\)\uff0c\u5247 \\(f(x)\\)\u00a0\u6703\u5047\u8a2d\u70ba \\(f(x) = f(3) + p(x &#8211; 3) + q(x &#8211; 3)(x &#8211; 2)\\)\u3002<\/p>\n<p>\u66f4\u68d2\u7684\u662f\uff0c\u9806\u8457\u9019\u6a23\u7684\u601d\u8def\uff0c\u8b80\u8005\u61c9\u8a72\u4e5f\u767c\u73fe\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f\u7684\u5f62\u5f0f\u5c0d\u65bc\u589e\u52a0\u65b0\u7684\u689d\u4ef6\uff0c\u8655\u7406\u4e0a\u65b9\u4fbf\u4e0d\u5c11\u3002\u4f8b\u5982\uff0c\u6211\u5011\u5728\u539f\u6709\u7684\\(A(1,7)\\)\uff0c\\(B(2,6)\\)\uff0c\\(C(3,11)\\) \u4e09\u9ede\uff0c\u518d\u52a0\u5165\u65b0\u7684\u89c0\u6e2c\u8cc7\u6599\u9ede \\(D(-1,28)\\)\uff0c\u8acb\u6c42\u51fa\u5716\u5f62\u6eff\u8db3\u9019\u56db\u9ede\u7684\u6700\u4f4e\u6b21\u591a\u9805\u5f0f\u51fd\u6578 \\(g(x)\\)\uff1f\u6709\u6c92\u6709\u8fa6\u6cd5\u5728\u5df2\u77e5\u51fd\u6578 \\(f(x)\\)\u00a0\u7684\u57fa\u790e\u4e0a\uff0c\u6c42\u51fa \\(g(x)\\)\u00a0\u5462\uff1f<\/p>\n<p>\u9996\u5148\uff0c\\(g(x)\\)\u00a0\u61c9\u8a72\u662f\u500b\u4e09\u6b21\u591a\u9805\u5f0f\u3002\u7531\u65bc\u6eff\u8db3 \\(g(1) = f(1) = 7\\)\uff0c\\(g(2) = f(2) = 6\\)\uff0c\\(g(3) = f(3) = 11\\)\u3002\u627f\u4e0a\u8a0e\u8ad6\uff0c\u6211\u5011\u53ef\u8a2d \\(g(x) = f(x) + c(x &#8211; 1)(x &#8211; 2)(x &#8211; 3)\\)\uff0c\u5c07 \\(g(-1)=28\\)\u00a0\u4ee3\u5165\uff0c\u53ef\u5f97 \\(c=-2\\)\u3002\u56e0\u6b64\uff0c<\/p>\n<p>\\(\\begin{array}{ll}g(x)&amp; = f(x) &#8211; 2(x &#8211; 1)(x &#8211; 2)(x &#8211; 3) \\\\&amp;= 7 &#8211; (x &#8211; 1) + 3(x &#8211; 1)(x &#8211; 2) &#8211; 2(x &#8211; 1)(x &#8211; 2)(x &#8211; 3)\\end{array}\\)<\/p>\n<p>\u4e86\u89e3\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f\u7684\u5f62\u5f0f\u6240\u860a\u6db5\u7684\u610f\u7fa9\u5f8c\uff0c\u61c9\u8a72\u5c31\u80fd\u638c\u63e1\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f\u7684\u5f62\u5f0f\uff0c\u9032\u800c\u6c42\u51fa\u5f85\u5b9a\u7684\u4fc2\u6578\u3002\u7136\u800c\uff0c\u5728\u3008\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f(1)\u3009\u4e2d\uff0c\u6211\u5011\u66fe\u8ac7\u53ca\u725b\u9813\u65e9\u6ce8\u610f\u5230\u63d2\u503c\u591a\u9805\u5f0f\u7684\u4fc2\u6578\u6709\u5176\u904b\u7b97\u898f\u5f8b(\u53ea\u662f\u4ed6\u6c92\u6709\u4ea4\u5f85\u5982\u4f55\u5f97\u5230)\u3002\u5728\u4e0b\u4e00\u7bc7\u6587\u7ae0\u3008\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f(3)\u3009\u4e2d\uff0c\u5c07\u4ecb\u7d39\u76ee\u524d\u6578\u503c\u5206\u6790\u4e2d\u6709\u95dc\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f\u4fc2\u6578\u7684\u904b\u7b97\u898f\u5247\uff0c\u4ee5\u53ca\u5e38\u7528\u7684\u7c21\u4fbf\u7b97\u6cd5\u3002<\/p>\n<p>\u9023\u7d50\uff1a<a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=57684\">\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f(3)<\/a><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u725b\u9813\u63d2\u503c\u591a\u9805\u5f0f (2)\u00a0(Newton Interpolating polynomial) \u81fa\u5317\u5e02\u7acb\u7b2c\u4e00\u5973\u5b50\u9ad8&hellip;<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[219,220,111],"tags":[474,423,7169],"class_list":["post-57608","post","type-post","status-publish","format-standard","hentry","category-math03","category-math03-01","category-mathematics00","tag-474","tag-423","tag-7169","loop-entry","cat-219","cat-220","cat-111","no-thumbnail"],"views":8613,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/57608","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=57608"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/57608\/revisions"}],"predecessor-version":[{"id":86854,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/57608\/revisions\/86854"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=57608"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=57608"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=57608"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}