{"id":459,"date":"2021-05-09T21:18:10","date_gmt":"2021-05-09T13:18:10","guid":{"rendered":"http:\/\/www.wayln.com\/?p=459"},"modified":"2021-05-10T21:32:00","modified_gmt":"2021-05-10T13:32:00","slug":"4-8-%e5%b7%ae%e5%88%86%e6%96%b9%e7%a8%8b%e4%b8%ad%e7%9a%84%e5%ba%94%e7%94%a8","status":"publish","type":"post","link":"https:\/\/www.wayln.com\/?p=459","title":{"rendered":"4.8 \u5dee\u5206\u65b9\u7a0b\u4e2d\u7684\u5e94\u7528"},"content":{"rendered":"<div id=\"toc_container\" class=\"toc_transparent no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u79bb\u6563\u65f6\u95f4\u4fe1\u53f7<\/a><\/li><li><a href=\"#S\"><span class=\"toc_number toc_depth_1\">2<\/span> \u4fe1\u53f7\u7a7a\u95f4S\u4e2d\u7684\u7ebf\u6027\u65e0\u5173\u6027<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">3<\/span> \u7ebf\u6027\u5dee\u5206\u65b9\u7a0b<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">4<\/span> \u7ebf\u6027\u5dee\u5206\u65b9\u7a0b\u7684\u89e3\u96c6<\/a><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">5<\/span> \u975e\u9f50\u6b21\u65b9\u7a0b<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">6<\/span> \u5316\u7b80\u6210\u4e00\u9636\u65b9\u7a0b\u7ec4<\/a><\/li><\/ul><\/div>\n<h1><span id=\"i\">\u79bb\u6563\u65f6\u95f4\u4fe1\u53f7<\/span><\/h1>\n<p>\u79bb\u6563\u65f6\u95f4\u4fe1\u53f7\u7684\u5411\u91cf\u7a7a\u95f4<span class=\"katex math inline\">S<\/span>\u57284.1\u8282\u4e2d\u5f15\u5165\uff0c<span class=\"katex math inline\">S<\/span>\u4e2d\u4e00\u4e2a<strong>\u4fe1\u53f7<\/strong>\u662f\u4e00\u4e2a\u53ea\u5b9a\u4e49\u5728\u6574\u6570\u4e0a\u7684\u51fd\u6570\uff0c\u540c\u65f6\u53ef\u7528\u4e00\u6570\u5217\u5c06\u5176\u76f4\u89c2\u5316\uff0c\u5373<span class=\"katex math inline\">&#92;{y_k&#92;}<\/span>\u3002\u4e0b\u56fe\u5c55\u793a\u4e86\u4e09\u4e2a\u5178\u578b\u7684\u4fe1\u53f7\uff0c\u5b83\u4eec\u7684\u901a\u9879\u5206\u522b\u662f<span class=\"katex math inline\">(0.7)^k,1^k\u548c(-1)^k<\/span><br \/>\n<a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/05\/wp_editor_md_1277d8caa34960b4727cba835f7b8d84.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/05\/wp_editor_md_1277d8caa34960b4727cba835f7b8d84.jpg\" alt=\"\" \/><\/a><\/p>\n<h1><span id=\"S\">\u4fe1\u53f7\u7a7a\u95f4S\u4e2d\u7684\u7ebf\u6027\u65e0\u5173\u6027<\/span><\/h1>\n<p>\u3000\u4e3a\u4e86\u7b80\u5316\u7b26\u53f7\uff0c\u6211\u4eec\u8003\u8651\u4e00\u4e2a\u4ec5\u5305\u542b\u4e09\u4e2a\u4fe1\u53f7<span class=\"katex math inline\">&#92;{u_k&#92;}&#92;{v_k&#92;}&#92;{w_k&#92;}<\/span>\u7684\u96c6\u5408S\uff0c\u5f53\u65b9\u7a0b<\/p>\n<p>&#8220;`math<br \/>\n c_1u_k+c_2v_k+c_3w_k=0\u3000\u5bf9\u6240\u6709k\u6210\u7acb \\tag{1}<br \/>\n &#8220;`<br \/>\n \u8574\u542b<span class=\"katex math inline\">c_1=c_2=c_3=0\u65f6\uff0c\\\\{u_k\\\\},\\\\{v_K\\\\},\\\\{w_k\\\\}<\/span>\u6070\u597d\u662f\u7ebf\u6027\u65e0\u5173\u7684\u3002\u8fd9\u91cc\u8bf4\u201c\u5bf9\u6240\u6709k\u6210\u7acb\u201d\u6307\u5bf9\u6240\u6709\u6574\u6570\u2014\u2014\u6b63\u6574\u6570\u3001\u8d1f\u6574\u6570\u548c0\u5747\u6210\u7acb\u3002\u6211\u4eec\u53ef\u80fd\u8003\u8651\u4ece<span class=\"katex math inline\">k=0<\/span>\u5f00\u59cb\u7684\u4fe1\u53f7\uff0c\u4f8b\u5982\uff0c\u8fd9\u65f6\u201c\u5bf9\u6240\u6709k\u6210\u7acb\u201d\u5c06\u8868\u793a\u5bf9\u6240\u6709<span class=\"katex math inline\">k \\ge 0<\/span>\u7684\u6574\u6570\u6210\u7acb\u3002<br \/>\n\u3000\u5047\u8bbe<span class=\"katex math inline\">c_1,c_2,c_3<\/span>\u6ee1\u8db3(1)\u5f0f\uff0c\u90a3\u4e48\u65b9\u7a0b(1)\u5bf9\u4efb\u610f\u4e09\u4e2a\u76f8\u90bb\u7684\u503c<span class=\"katex math inline\">k,k+1\u548ck+2<\/span>\u6210\u7acb\uff0c\u8fd9\u6837(1)\u8574\u542b<br \/>\n &#8220;`math<br \/>\n \\begin{align*}<br \/>\n c_1u_{k+1}+c_2v_{k+1}+c_3w_{k+1}=0\u3000\u5bf9\u6240\u6709k\u6210\u7acb\\\\<br \/>\n c_1u_{k+2}+c_2v_{k+2}+c_3w_{k+2}=0\u3000\u5bf9\u6240\u6709k\u6210\u7acb\\\\<br \/>\n \\end{align*}<br \/>\n &#8220;`<br \/>\n \u4ece\u800c<span class=\"katex math inline\">c_1,c_2,c_3<\/span>\u6ee1\u8db3<\/p>\n<div class=\"katex math multi-line no-emojify\">\\left[\\begin{array}{lll}u_k&amp;v_k&amp;w_k\\\\<br \/>\nu_{k+1}&amp;v_{k+1}&amp;w_{k+1}\\\\<br \/>\nu_{k+2}&amp;v_{k+2}&amp;w_{k+2}\\\\<br \/>\n\\end{array}\\right]<\/p>\n<p>\\left[\\begin{array}{l}c_1\\\\<br \/>\nc_2\\\\<br \/>\nc_3\\\\<br \/>\n\\end{array}\\right]<br \/>\n=<br \/>\n\\left[\\begin{array}{l}0\\\\<br \/>\n0\\\\<br \/>\n0\\\\<br \/>\n\\end{array}\\right]\u3000\u5bf9\u6240\u6709k\u6210\u7acb\u3000\\tag{2}\n<\/p><\/div>\n<p>\u8fd9\u4e2a\u65b9\u7a0b\u7ec4\u7684\u7cfb\u6570\u77e9\u9635\u6210\u4e3a\u4fe1\u53f7\u7684<strong>Casorati\u77e9\u9635<\/strong>\uff0c\u8fd9\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\u6210\u4e3a<span class=\"katex math inline\">&#92;{u_K&#92;},&#92;{v_K&#92;},&#92;{w_K&#92;}<\/span>\u7684<strong>Casorati\u884c\u5217\u5f0f<\/strong>\u3002\u5982\u679c\u5bf9\u81f3\u5c11\u4e00\u4e2a<span class=\"katex math inline\">k<\/span>\u503cCasorati\u77e9\u9635\u53ef\u9006\uff0c\u5219(2)\u5c06\u8574\u542b<span class=\"katex math inline\">c_1=c_2=c_3=0<\/span>,\u8fd9\u5c31\u8bc1\u660e\u8fd9\u4e09\u4e2a\u4fe1\u53f7\u662f\u7ebf\u6027\u65e0\u5173\u7684\u3002<br \/>\n\u3000\u82e5Casorati\u77e9\u9635\u4e0d\u53ef\u9006\uff0c\u76f8\u5e94\u7684\u4fe1\u53f7\u901a\u8fc7\u68c0\u6d4b\u53ef\u80fd\u7ebf\u6027\u76f8\u5173\u4e5f\u53ef\u80fd\u4e0d\u662f\u7ebf\u6027\u76f8\u5173\u3002\u4f46\u53ef\u4ee5\u8bc1\u660e\uff0c\u5982\u679c\u8fd9\u4e9b\u4fe1\u53f7\u662f\u540c\u4e00\u4e2a\u9f50\u6b21\u5dee\u5206\u65b9\u7a0b\u7684\u6240\u6709\u89e3\uff0c\u5219Casorati\u77e9\u9635\u5bf9\u6240\u6709k\u662f\u53ef\u9006\u7684\u4e14\u8fd9\u4e9b\u4fe1\u53f7\u662f\u7ebf\u6027\u65e0\u5173\u7684\uff0c\u5426\u5219Casorati\u77e9\u9635\u5bf9\u6240\u6709k\u90fd\u4e0d\u53ef\u9006\u4e14\u8fd9\u4e9b\u4fe1\u53f7\u662f\u7ebf\u6027\u76f8\u5173\u7684\u3002<\/p>\n<h1><span id=\"i-2\">\u7ebf\u6027\u5dee\u5206\u65b9\u7a0b<\/span><\/h1>\n<p>\u3000\u7ed9\u5b9a\u6570\u91cf<span class=\"katex math inline\">a_0,\\dots,a_n,a_0\u548ca_n<\/span>\u4e0d\u4e3a\u96f6\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u4fe1\u53f7<span class=\"katex math inline\">z_k<\/span>,\u65b9\u7a0b<\/p>\n<p>&#8220;`math<br \/>\n a_0y_{k+n}+a_1y_{k+n-1}+\\dots+a_{n-1}y_{k+1}+a_ny_k=z_k\u3000\u5bf9\u6240\u6709k\u6210\u7acb\u3000\\tag{3}<br \/>\n &#8220;`<br \/>\n \u79f0\u4e3a\u4e00\u4e2a**n\u9636\u7ebf\u6027\u5dee\u5206\u65b9\u7a0b(\u6216\u7ebf\u6027\u9012\u5f52\u5173\u7cfb)**\u3002\u4e3a\u4e86\u7b80\u5316\uff0c<span class=\"katex math inline\">a_0<\/span>\u901a\u5e38\u53d6\u4e3a1\uff0c\u82e5<span class=\"katex math inline\">\\\\{z_k\\\\}<\/span>\u662f\u96f6\u5e8f\u5217\uff0c\u5219\u65b9\u7a0b\u662f**\u9f50\u6b21\u7684**\uff1b\u5426\u5219\uff0c\u65b9\u7a0b\u662f**\u975e\u9f50\u6b21\u7684**\u3002<\/p>\n<p>\u3000<strong>\u4f8b3<\/strong>\u3000\u5728\u6570\u5b57\u4fe1\u53f7\u5904\u7406\u4e2d\uff0c\u50cf\u4e0a\u9762(3)\u90a3\u6837\u7684\u5dee\u5206\u65b9\u7a0b\u7528\u6765\u63cf\u8ff0\u4e00\u4e2a\u7ebf\u6027\u6ee4\u6ce2\u5668\uff0c<span class=\"katex math inline\">a_0,\\dots,a_n<\/span>\u79f0\u4e3a\u6ee4\u6ce2\u5668\u7cfb\u6570\uff0c\u82e5\u5c06<span class=\"katex math inline\">&#92;{y_k&#92;}<\/span>\u770b\u505a\u8f93\u5165\uff0c<span class=\"katex math inline\">&#92;{z_k&#92;}<\/span>\u770b\u4f5c\u8f93\u51fa\uff0c\u5219\u5bf9\u5e94\u9f50\u6b21\u65b9\u7a0b\u7684\u89e3\u662f\u8fc7\u6ee4\u6389\u7684\u4fe1\u53f7\uff0c\u5e76\u88ab\u53d8\u6362\u4e3a\u96f6\u4fe1\u53f7\uff0c\u8ba9\u6211\u4eec\u5411\u5982\u4e0b\u6ee4\u6ce2\u5668\u8f93\u5165\u4e24\u4e2a\u4e0d\u540c\u7684\u4fe1\u53f7\uff1a<\/p>\n<p>&#8220;`math<br \/>\n 0.35y_{k+2}=0.5y_{k+1}+0.35y_k=z_k<br \/>\n &#8220;`<br \/>\n \u8fd9\u91cc0.35\u662f<span class=\"katex math inline\">\\sqrt{2}\/4<\/span>\u7684\u7b80\u5199\uff0c\u7b2c\u4e00\u4e2a\u4fe1\u53f7\u662f\u7531\u8fde\u7eed\u4fe1\u53f7<span class=\"katex math inline\">y=\\cos(\\pi t\/4)<\/span>\u5728\u6574\u6570\u503ct\u62bd\u6837\u800c\u751f\u6210\uff0c\u5982\u4e0b\u56fe\u6240\u793a\u3002\u79bb\u6563\u4fe1\u53f7\u662f<span class=\"katex math inline\">\\\\{y_k\\\\}=\\\\{\\dots,\\cos(\\pi \/4),\\cos(2\\pi\/4),\\cos(3\\pi\/4),\\dots\\\\}<\/span>\u3002<br \/>\n \u4e3a\u4e86\u7b80\u5355\uff0c\u7528<span class=\"katex math inline\">\\pm0.7<\/span>\u4ee3\u66ff<span class=\"katex math inline\">\\pm \\sqrt{2}\/2<\/span>,\u4ece\u800c<br \/>\n &#8220;`math<br \/>\n \\{y_k\\}=\\{\\dots,\\underbrace{1}_{k=0},0.7,0,-0.7,-1,-0.7,0,0.7,1,0.7,0,\\dots\\}<br \/>\n &#8220;`<br \/>\n [![](http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/05\/wp_editor_md_2264a70b8b94d627b8bd874775f36702.jpg)](http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/05\/wp_editor_md_2264a70b8b94d627b8bd874775f36702.jpg)<br \/>\n \u4e0b\u8868\u5c55\u793a\u51fa\u8f93\u51fa\u5e8f\u5217<span class=\"katex math inline\">\\\\{z_k\\\\}<\/span>\u7684\u4e00\u4e2a\u8ba1\u7b97\u3002\u8fd9\u91cc0.35(0.7)\u662f<span class=\"katex math inline\">(\\sqrt{2}\/4)(\\sqrt{2}\/2)=0.25<\/span>\u7684\u7b80\u5199\uff0c\u5c06<span class=\"katex math inline\">\\\\{z_k\\\\}<\/span>\u79fb\u52a8\u610f\u5411\uff0c\u8f93\u51fa\u5c31\u6210\u4e3a<span class=\"katex math inline\">\\\\{y_k\\\\}<\/span><br \/>\n [![](http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/05\/wp_editor_md_943b6171584943b13bd1588235dfcd45.jpg)](http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/05\/wp_editor_md_943b6171584943b13bd1588235dfcd45.jpg)<br \/>\n \u4e8e\u662f\u4e00\u4e2a\u4e0d\u540c\u7684\u8f93\u5165\u4fe1\u53f7\u7531\u66f4\u9ad8\u9891\u7387\u4fe1\u53f7<span class=\"katex math inline\">y=cos(3\\pi t\/4)<\/span>\u751f\u6210\uff0c\u89c1\u4e0a\u56feb\u3002\u7528\u4e0e\u524d\u9762\u76f8\u540c\u7684\u62bd\u6837\u7387\u53bb\u62bd\u6837\uff0c\u6211\u4eec\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\u8f93\u5165\u5e8f\u5217\uff1a<br \/>\n &#8220;`math<br \/>\n \\{w_k\\}=\\{\\dots,\\underbrace{1}_{k=0},-0.7,0,0.7,-1,0.7,0,-0.7,1,-0.7,0,\\dots \\}<br \/>\n &#8220;`<br \/>\n \u5f53\u5c06<span class=\"katex math inline\">\\\\{w_k\\\\}<\/span>\u8f93\u5165\u7ed9\u6ee4\u6ce2\u5668\uff0c\u5219\u8f93\u51fa\u662f\u96f6\u5e8f\u5217\uff0c\u82e5\u4e00\u4e2a\u6ee4\u6ce2\u5668\u4f7f<span class=\"katex math inline\">\\\\{y_k\\\\}<\/span>\u80fd\u591f\u901a\u8fc7\uff0c\u4f46\u5c06\u9ad8\u9891\u7684<span class=\"katex math inline\">\\\\{w_k\\\\}<\/span>\u622a\u6389\uff0c\u5219\u79f0\u8be5\u6ee4\u6ce2\u5668\u4e3a**\u4f4e\u901a\u6ee4\u6ce2\u5668**\u3002<br \/>\n\u3000\u5728\u8bb8\u591a\u5e94\u7528\u4e2d\uff0c\u5e8f\u5217<span class=\"katex math inline\">\\\\{z_k\\\\}<\/span>\u7531\u5dee\u5206\u65b9\u7a0b(3)\u7684\u53f3\u7aef\u786e\u5b9a\uff0c\u6ee1\u8db3(3)\u7684\u4e00\u4e2a<span class=\"katex math inline\">\\\\{y_k\\\\}<\/span>\u6210\u4e3a\u8fd9\u4e2a\u65b9\u7a0b\u7ec4\u7684\u4e00\u4e2a\u89e3\u3002<\/p>\n<h1><span id=\"i-3\">\u7ebf\u6027\u5dee\u5206\u65b9\u7a0b\u7684\u89e3\u96c6<\/span><\/h1>\n<p>\u3000\u7ed9\u5b9a<span class=\"katex math inline\">a_1,\\dots,a_n<\/span>\uff0c\u8003\u8651\u6620\u5c04<span class=\"katex math inline\">T:S \\rightarrow S<\/span>,\u5c06\u4fe1\u53f7<span class=\"katex math inline\">&#92;{y_k&#92;}<\/span>\u53d8\u6362\u5230\u4fe1\u53f7<span class=\"katex math inline\">&#92;{w_k&#92;}<\/span>\uff0c\u7531\u4e0b\u5f0f\u7ed9\u51fa<\/p>\n<p>&#8220;`math<br \/>\n w_k=y_{k+n}+a_1y_{k+n-1}+\\dots+a_{n-1}y_{k+1}+a_ny_k<br \/>\n &#8220;`<br \/>\n \u5bb9\u6613\u9a8c\u8bc1T\u662f\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\uff0c\u8fd9\u8574\u542b\u5176\u6b21\u65b9\u7a0b<br \/>\n &#8220;`math<br \/>\n y_{k+n}+a_1y_{k+n-1}+\\dots+a_{n-1}y_{k+1}+a_ny_k=0\u3000\u5bf9\u6240\u6709k\u6210\u7acb<br \/>\n &#8220;`<br \/>\n \u7684\u89e3\u96c6\u662fT\u7684\u6838\uff08\u7ecfT\u6620\u5c04\u5230\u96f6\u4fe1\u53f7\u7684\u4fe1\u53f7\u7684\u96c6\u5408\uff09\uff0c\u8fdb\u800c\u8fd9\u4e2a\u89e3\u96c6\u662fS\u7684\u4e00\u4e2a\u5b50\u7a7a\u95f4\uff0c\u4efb\u4f55\u89e3\u7684\u7ebf\u6027\u7ec4\u5408\u4ecd\u7136\u662f\u89e3\u3002<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u740616<\/strong>\u3000\u82e5<span class=\"katex math inline\">a_n \\ne 0<\/span>\u4e14<span class=\"katex math inline\">&#92;{z_k&#92;}<\/span>\u7ed9\u5b9a,\u53ea\u8981<span class=\"katex math inline\">y_0,\\dots,y_{n-1}<\/span>\u7ed9\u5b9a\uff0c\u65b9\u7a0b<\/p>\n<div class=\"katex math multi-line no-emojify\">  y_{k+n}+a_1y_{k+n-1}+ \\dots+ a_{n-1}y_{k+1}+a_ny_k=z_k\u3000\u5bf9\u6240\u6709k\u6210\u7acb\u3000\\tag{7}\n  <\/div>\n<p>  \u6709\u552f\u4e00\u89e3\u3002<\/p>\n<p>  <strong>\u5b9a\u740617<\/strong>\u3000n\u9636\u9f50\u6b21\u7ebf\u6027\u5dee\u5206\u65b9\u7a0b<\/p>\n<div class=\"katex math multi-line no-emojify\">y_{k+n}+a_1y_{k+n-1}+\\dots+a_{n-1}y_{k+1}+a_ny_k=0\u3000\u5bf9\u6240\u6709k\u6210\u7acb\\tag{10}\n  <\/div>\n<p>  \u7684\u89e3\u96c6H\u662f\u4e00\u4e2an\u7ef4\u5411\u91cf\u7a7a\u95f4\n<\/p><\/blockquote>\n<h1><span id=\"i-4\">\u975e\u9f50\u6b21\u65b9\u7a0b<\/span><\/h1>\n<p>\u975e\u9f50\u6b21\u5dee\u5206\u65b9\u7a0b<\/p>\n<div class=\"katex math multi-line no-emojify\">y_{k+n}+a_1y_{k+n-1}+\\dots+a_{n-1}y_{k+1}+a_ny_k=z_k\u3000\u5bf9\u6240\u6709k\u6210\u7acb\\tag{11}\n<\/div>\n<p>\u7684\u901a\u89e3\u80fd\u5199\u6210(11)\u7684\u4e00\u4e2a\u7279\u89e3\u52a0\u4e0a\u5bf9\u5e94\u9f50\u6b21\u5dee\u5206\u65b9\u7a0b(10)\u7684\u4e00\u4e2a\u57fa\u7840\u89e3\u7cfb\u7684\u4efb\u610f\u7ebf\u6027\u7ec4\u5408\u3002<\/p>\n<h1><span id=\"i-5\">\u5316\u7b80\u6210\u4e00\u9636\u65b9\u7a0b\u7ec4<\/span><\/h1>\n<p>\u7814\u7a76n\u9636\u9f50\u6b21\u7ebf\u6027\u5dee\u5206\u65b9\u7a0b\u7684\u73b0\u4ee3\u65b9\u6cd5\u662f\u7528\u7b49\u4ef7\u7684\u4e00\u9636\u5dee\u5206\u65b9\u7a0b\u7ec4\u4ee3\u66ff\u5b83\uff0c\u5176\u4e2d\u4e00\u9636\u5dee\u5206\u65b9\u7a0b\u5199\u6210\u5982\u4e0b\u5f62\u52bf\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">x_{k+1}=Ax_k,\u3000\u5bf9\u6240\u6709k\u6210\u7acb\n<\/div>\n<p>\u8fd9\u91cc\u5411\u91cf<span class=\"katex math inline\">x_k<\/span>\u5728<span class=\"katex math inline\">R^n<\/span>\u4e2d\uff0c<span class=\"katex math inline\">A<\/span>\u662f\u4e00\u4e2a<span class=\"katex math inline\">nxn<\/span>\u77e9\u9635<\/p>\n<p>\u4e00\u822c\u800c\u8a00\uff0c\u65b9\u7a0b<\/p>\n<div class=\"katex math multi-line no-emojify\">y_{k+n}+a_1y_{k+n-1}+\\dots+a_{n-1}y_{k+1}+a_ny_k=0,\u3000\u5bf9\u6240\u6709k\u6210\u7acb\n<\/div>\n<p>\u53ef\u91cd\u5199\u6210<span class=\"katex math inline\">x_{k+1}=Ax_k<\/span>,\u5bf9\u6240\u6709k\u6210\u7acb\uff0c\u8fd9\u91cc<\/p>\n<div class=\"katex math multi-line no-emojify\">x_k=\\left[\\begin{array}{l}y_k\\\\y_{k+1}\\\\\\vdots\\\\y_{k+n-1}\\end{array}\\right]\n<\/div>\n<div class=\"katex math multi-line no-emojify\">A=\\left[\\begin{array}{ccccc}0&amp;1&amp;0&amp;\\dots&amp;0\\\\<br \/>\n0&amp;0&amp;1&amp;&amp;0\\\\<br \/>\n\\vdots&amp;&amp;&amp;\\ddots&amp;\\vdots\\\\<br \/>\n0&amp;0&amp;0&amp;&amp;1\\\\<br \/>\n-a_n&amp;-a_{n-1}&amp;-a_{n-2}&amp;\\dots&amp;-a_1\\\\<br \/>\n\\end{array}\\right]\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u79bb\u6563\u65f6\u95f4\u4fe1\u53f72 \u4fe1\u53f7\u7a7a\u95f4S\u4e2d\u7684\u7ebf\u6027\u65e0\u5173\u60273 \u7ebf\u6027\u5dee\u5206\u65b9\u7a0b4 \u7ebf\u6027\u5dee\u5206\u65b9\u7a0b\u7684\u89e3\u96c65 \u975e\u9f50\u6b21\u65b9 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":410,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-459","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-21","category-22","category-26"],"_links":{"self":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/459","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=459"}],"version-history":[{"count":10,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/459\/revisions"}],"predecessor-version":[{"id":476,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/459\/revisions\/476"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/410"}],"wp:attachment":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=459"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}