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computing.jemdoc
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# jemdoc: menu{MENU}{computing.html}, nofooter
= Yao Zhang - Computing
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Scientific computing is an interdisciplinary field that employs numerical methods and computational technologies to address complex scientific problems. It consists of three core components: numerical linear algebra, numerical optimization, and numerical solutions of differential equations.
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Numerical linear algebra focuses on solving matrix and vector problems, such as linear equations and eigenvalue problems. This area provides essential tools for various applications in science and engineering, particularly when dealing with large, sparse matrices. Building on this foundation, numerical optimization seeks to find the optimal solution for functions, with or without constraints. This component is crucial in fields like machine learning and data analysis, where optimization techniques are instrumental in model training and decision-making.
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Numerical solutions of differential equations involve solving ordinary and partial differential equations using techniques like finite difference, finite element, and finite volume methods. These approaches are vital for modeling physical phenomena, especially in fluid dynamics and heat transfer. Together, these components form the backbone of scientific computing, enabling the simulation and resolution of complex real-world problems across various disciplines.
== Matrix Computation
- [https://mp.weixin.qq.com/s/HoypzSAq-5odXJWE3o79nA 01] ~~ [https://mp.weixin.qq.com/s/gorfJ5CIRegl7VpH2crmLw 02] ~~ [https://mp.weixin.qq.com/s/zU3Z_H0lc-PiERj8qHdmMA 03] ~~ [https://mp.weixin.qq.com/s/_H8-sBe4VIZyhBTh3-0wAg 04] ~~ [https://mp.weixin.qq.com/s/15GDHM_C6NDzdDmihcCX8Q 05] ~~ [https://mp.weixin.qq.com/s/FhISpeaMwFl413007bOkPg 06] ~~ [https://mp.weixin.qq.com/s/KdgDwiWWy-w-_TBjPKDbDA 07] ~~ [https://mp.weixin.qq.com/s/BF3UmupZ1oVrdD1lVJhA8Q 08] ~~ [https://mp.weixin.qq.com/s/PFVkSYV8wP5G7NeSLvHwWQ 09] ~~ [https://mp.weixin.qq.com/s/s7xN1p_1E0NGJNOqqVip_w 10] ~~ [https://mp.weixin.qq.com/s/OyFJIQ1Z2zMFTgarQF0W8w 11] ~~ [https://mp.weixin.qq.com/s/n0MbV66CRESunyqycQ9upw 12] ~~ [https://mp.weixin.qq.com/s/znQ3_OLoQ8bAL8tGsNnmUQ 13] ~~ [https://mp.weixin.qq.com/s/I9e8g5BKCf_9EZM9dD8vvw 14] ~~ [https://mp.weixin.qq.com/s/1Yo3RKyvORy1bjpcp7QvKg 15] ~~ [https://mp.weixin.qq.com/s/q9fxtV302DGZPksWOCrupQ 16] ~~ [https://mp.weixin.qq.com/s/1HAcMwRwdJI1fTvaIwMhHQ 17] ~~ [https://mp.weixin.qq.com/s/_4j4RcJRvZ_quaW_kA6vsQ 18] ~~ [https://mp.weixin.qq.com/s/62h-um7aSRYQRT9FxaHOqQ 19] ~~ [https://mp.weixin.qq.com/s/U6RE8wc9VeW9PXqNmOlSfw 20] ~~ [https://mp.weixin.qq.com/s/JjNX_0598Z12nlB5Mk6Teg 21] ~~ [https://mp.weixin.qq.com/s/53QB3pVUSS17RPYRQ4yWZQ 22] ~~ [https://mp.weixin.qq.com/s/G2TLU-VxZEA9RWAEo4a2Yw 23] ~~ [https://mp.weixin.qq.com/s/zlSZ8rlI5vCBqANUrRpfAw 24] ~~ [https://mp.weixin.qq.com/s/XdZRJ0NazKtqLP5JUuUi5A 25] ~~ [https://mp.weixin.qq.com/s/3Ts4sbIQ5Z8uCTPHZtXpoA 26] ~~ [https://mp.weixin.qq.com/s/wZXGX8derlrSF7OgBEtqXA 27] ~~ [https://mp.weixin.qq.com/s/Lbi4eZ9TITKjK-g1NqYlHQ 28] ~~ [https://mp.weixin.qq.com/s/UfNSU6b7kq9TTNp4646Urg 29] ~~ [https://mp.weixin.qq.com/s/nOjpy69rMj8o1MyC5_e02g 30] ~~ [https://mp.weixin.qq.com/s/y4HAP7JMz4b74Y4wp8VRew 31] ~~ [https://mp.weixin.qq.com/s/EXQGekUW_P1raETO93bI1w 32] ~~ [https://mp.weixin.qq.com/s/JvAO5B-8sIZWRA-qDaRqxw 33] ~~ [https://mp.weixin.qq.com/s/OrOnE_MIPATl4tp8OxYE7A 34] ~~ [https://mp.weixin.qq.com/s/8jJILW9ptkHEhD-NIz7fmA 35]
\n
- [https://mp.weixin.qq.com/s/shiLIlt7v88EtiYW6RIxwQ 36] ~~ [https://mp.weixin.qq.com/s/Bgjm78XlmPO6wKZQWL2s1A 37] ~~ [https://mp.weixin.qq.com/s/CT8ZZXSFkk4oqVvXgwabfA 38] ~~ [https://mp.weixin.qq.com/s/qXLxtBQbDx0ANJyoNwAZUw 39] ~~ [https://mp.weixin.qq.com/s/I6PM1sZn-Zo9OCcFQahkvw 40] ~~ [https://mp.weixin.qq.com/s/jntUkD3An1f_qOaZ0CKPCg 41] ~~ [https://mp.weixin.qq.com/s/hPIZVJ_qpSwZM0BiIzHeIg 42] ~~ [https://mp.weixin.qq.com/s/fQ1iWb5ZxRjsfreQFtzP0g 43] ~~ [https://mp.weixin.qq.com/s/tebKSkxoHehaUi2hAQkb4w 44] ~~ [https://mp.weixin.qq.com/s/_dRzZMCKQsYwpvN3MNSqWQ 45] ~~ [https://mp.weixin.qq.com/s/q9mGoLhkDvtHcmLOwf81zg 46] ~~ [https://mp.weixin.qq.com/s/wE8WhMDKVEATYMIQ23PH-g 47] ~~ [https://mp.weixin.qq.com/s/XiElXtJh1VQ8mDhz5h3urw 48] ~~ [https://mp.weixin.qq.com/s/SGjUTpxlTIch-ipLftgzJQ 49]
\n
- [./doc/note/computing/matrixComputations.pdf Lecture Notes of Matrix Computations]
== Numerical Optimization
- [https://mp.weixin.qq.com/s/IReWeQLHKG9hnLHg4M1nHg 01] ~~ [https://mp.weixin.qq.com/s/l-7gmKGXNymbemX_C4cyDA 02] ~~ [https://mp.weixin.qq.com/s/LE39JddJZ5pux5igyMxfcg 03] ~~ [https://mp.weixin.qq.com/s/akWNb9M-0Gd8IHfFqrrFQw 04] ~~ [https://mp.weixin.qq.com/s/laUwMJzzfv1EQqduO8KdjA 05] ~~ [https://mp.weixin.qq.com/s/ey48Gpu4PHzMe6htKq4VnQ 06] ~~ [https://mp.weixin.qq.com/s/HZsk8z_-zMlUjJ2sUKXJWA 07] ~~ [https://mp.weixin.qq.com/s/cKjOCBSK5uXxpCI06w6msQ 08] ~~ [https://mp.weixin.qq.com/s/dTZ0hjyCMYOgIcvon0JEWQ 09] ~~ [https://mp.weixin.qq.com/s/ZVybCoT0_01gxb5JTv-gBg 10] ~~ [https://mp.weixin.qq.com/s/JsmWr-e3FyKLAsXbgdzviw 11] ~~ [https://mp.weixin.qq.com/s/CPGm-sHdAvNT9ja4y_H-eQ 12] ~~ [https://mp.weixin.qq.com/s/yx3Htz7ocman1FnFf8larQ 13] ~~ [https://mp.weixin.qq.com/s/S8HGg2U7SyThB13TukEMkw 14] ~~ [https://mp.weixin.qq.com/s/fOMlWSdFYUgyvC_otjq2GA 15] ~~ [https://mp.weixin.qq.com/s/9SV_nD9Qdh8jw6y5FLkMgQ 16] ~~ [https://mp.weixin.qq.com/s/tG4j842QlXkLjb3VSyorcA 17] ~~ [https://mp.weixin.qq.com/s/WdhediSm21GgTXP9mYWIGw 18] ~~ [https://mp.weixin.qq.com/s/pRerTeHjulQSDU86AX2BlA 19] ~~ [https://mp.weixin.qq.com/s/CcfMHmYYloy7jb7PJRQeWQ 20] ~~ [https://mp.weixin.qq.com/s/DtueOrT0ms9xqQfILcrRdg 21] ~~ [https://mp.weixin.qq.com/s/IDy2daxQZJQJ-FoEJYMrJg 22] ~~ [https://mp.weixin.qq.com/s/x2_TgfWb_fQZ04g6kJGYpw 23] ~~ [https://mp.weixin.qq.com/s/IQ51JGrBMif0Vy2Y2hP2IQ 24] ~~ [https://mp.weixin.qq.com/s/y7ugFajLCF6G5Zac4jHNXw 25] ~~ [https://mp.weixin.qq.com/s/kXZXUCa2SzcDXUog4UTKLg 26] ~~ [https://mp.weixin.qq.com/s/sryWvoEQ91QmVqyp6YJlng 27] ~~ [https://mp.weixin.qq.com/s/eoqx3ir7PGdyOAIW70-N_w 28] ~ [https://mp.weixin.qq.com/s/oQC3g8fLHjx3Qwv4aTiSjQ 29] ~~ [https://mp.weixin.qq.com/s/8Bb1IAxGLQgnodi6FnVQMQ 30] ~~ [https://mp.weixin.qq.com/s/QlZLiw82Sd8UEK6v0BGnIQ 31] ~~ [https://mp.weixin.qq.com/s/un5l3XAhSrbJL5Pp3IzXNg 32] ~~ [https://mp.weixin.qq.com/s/-REkRJkSM_yv2THIdQJo9w 33] ~~ [https://mp.weixin.qq.com/s/wE2y4syp1CysZ7mZVYpOXQ 34] ~~ [https://mp.weixin.qq.com/s/5nA3Hy2J7TaJ-5DdiEjHGg 35]
\n
- [https://mp.weixin.qq.com/s/0Qq2h9XAkeXOxAUYY2dxyA 36] ~~ [https://mp.weixin.qq.com/s/gamZ2vtfCJ4di0m86tWGcQ 37] ~~ [https://mp.weixin.qq.com/s/Zsp48otEmTjAr8TF8Kg0Zg 38] ~~ [https://mp.weixin.qq.com/s/j1j5lHWHUuSTcGu61AybJw 39] ~~ [https://mp.weixin.qq.com/s/RoVCf0bGgWcRSzNceAHD_g 40] ~~ [https://mp.weixin.qq.com/s/dBpcIh9NpWZEa1guhIOzjg 41] ~~ [https://mp.weixin.qq.com/s/WIdSr2JDXFDMGWCZLEnY9g 42] ~~ [https://mp.weixin.qq.com/s/G69mAbE1Fi6XhKYh1jflpQ 43] ~~ [https://mp.weixin.qq.com/s/S66cW2lsLI2jMcAM_CTekg 44] ~~ [https://mp.weixin.qq.com/s/-b0myxDR-lBzviJEetBX8w 45] ~~ [https://mp.weixin.qq.com/s/w0NI3Z3iNVrf7OlaA3lwpA 46] ~~ [https://mp.weixin.qq.com/s/cTwTDLtVw1KW5aCXYEC54A 47] ~~ [https://mp.weixin.qq.com/s/PcojiHRknKUzGX4IqRjozQ 48] ~~ [https://mp.weixin.qq.com/s/ElWz3vqDpX7Fua5_mkIwiQ 49] ~~ [https://mp.weixin.qq.com/s/Fbq_Clm54g7kziBpENjU1w 50] ~~ [https://mp.weixin.qq.com/s/T6e0q70Jr2nVOUFU0NqgSA 51] ~~ [https://mp.weixin.qq.com/s/vaZYqUbdYIJX77JwVdZ-yg 52] ~~ [https://mp.weixin.qq.com/s/3Lo1sX7q2y_vN6-5oqFW3g 53] ~~ [https://mp.weixin.qq.com/s/yYLa4SLn-zccuS2npmGx2A 54] ~~ [https://mp.weixin.qq.com/s/e2SzhfY7-IwUe-2nqrfjMg 55] ~~ [https://mp.weixin.qq.com/s/HZ0kMZmqGEH8jCPqF_xCGg 56] ~~ [https://mp.weixin.qq.com/s/VPCKkaKXnoz-64mytiXgaw 57] ~~ [https://mp.weixin.qq.com/s/L1WC45lRyAttALwyKzgd1A 58]
== Numerical Ordinary Differential Equations
- [https://mp.weixin.qq.com/s/EQUWi-8WT_8X3UDoRPA83Q 01] ~~ [https://mp.weixin.qq.com/s/1oLV7c--xs4F2t0IyZHqXA 02] ~~ [https://mp.weixin.qq.com/s/QL1Leh1b-KmyJ6OERhe48g 03] ~~ [https://mp.weixin.qq.com/s/QGB89sWz0vXR8xFMVmQraA 04] ~~ [https://mp.weixin.qq.com/s/20gag60tj9WdZDf__sGCSw 05] ~~ [https://mp.weixin.qq.com/s/gIMmmqXJt3bsBbJnLGTkaw 06] ~~ [https://mp.weixin.qq.com/s/MQxQsRyw60AbQFJLSDQChw 07] ~~ [https://mp.weixin.qq.com/s/73-ePp73c-fCBGw21tp7GQ 08] ~~ [https://mp.weixin.qq.com/s/mvfitTafsUi2SpeO8qTUgg 09] ~~ [https://mp.weixin.qq.com/s/jrpXgVS2eNRraACLBhTl0Q 10] ~~ [https://mp.weixin.qq.com/s/QdegoG2Z1A51bLlxO65vFQ 11] ~~ [https://mp.weixin.qq.com/s/wx_DMkqK_P3fXj8LCzahig 12] ~~ [https://mp.weixin.qq.com/s/rmTt6w39AIxHEEcB4wMpKQ 13] ~~ [https://mp.weixin.qq.com/s/buu85csZDveBBm54hQ1sGg 14] ~~ [https://mp.weixin.qq.com/s/O4wMTFqqhkinQGd7lsK4RA 15] ~~ [https://mp.weixin.qq.com/s/oFWLRPT4fRVW61e19ytkoQ 16] ~~ [https://mp.weixin.qq.com/s/60BXJe_Dz6co93eXRmM3xw 17] ~~ [https://mp.weixin.qq.com/s/b0586vQUl_osZI_ddw1BTQ 18] ~~ [https://mp.weixin.qq.com/s/BMWaPPq0jE28BV7m7eB4tw 19] ~~ [https://mp.weixin.qq.com/s/4IGer4Fu-24ycGfzuPrVfg 20] ~~ [https://mp.weixin.qq.com/s/TMivT0BGux95pihX8lud7Q 21] ~~ [https://mp.weixin.qq.com/s/PLwNxlCApcl535a8T-A-Qg 22] ~~ [https://mp.weixin.qq.com/s/_Yv7H9t_KMmHFobgWdwGPQ 23] ~~ [https://mp.weixin.qq.com/s/efvMAg0Xr7X6TFz0j2-tKw 24] ~~ [https://mp.weixin.qq.com/s/K5-iNNHyreSHfJemugGLtQ 25] ~~ [https://mp.weixin.qq.com/s/a3Zir6alVr2dqLcHjgXo9g 26] ~~ [https://mp.weixin.qq.com/s/_rSTT_tggZ8O-gc6cVHYvw 27] ~~ [https://mp.weixin.qq.com/s/_MQNfK9tbqLQMLp9tMyQmA 28] ~~ [https://mp.weixin.qq.com/s/6Inho55GcS_1b3vi7KmP6A 29] ~~ [https://mp.weixin.qq.com/s/EXDlflH8zkY7iKhWy6ARWg 30] ~~ [https://mp.weixin.qq.com/s/ecqyqtUOY2VS0SHulTc6QQ 31] ~~ [https://mp.weixin.qq.com/s/c3iV2TaqVrqRNcJAn95pGA 32] ~~ [https://mp.weixin.qq.com/s/yzE_miN-vMPOmHJGOX9Z2A 33] ~~ [https://mp.weixin.qq.com/s/53uJ5FcoKqk-iZ5tsf4HIw 34] ~~ [https://mp.weixin.qq.com/s/LuT6F7kCo0Skq72lGEMoXQ 35]
\n
- [https://mp.weixin.qq.com/s/mfhKURwrQWUEb6ZhjDufKA 36] ~~ [https://mp.weixin.qq.com/s/TJb2OAhAzIvdY07eKEFfkg 37] ~~ [https://mp.weixin.qq.com/s/9TS-itxVhLSvMqbuOuPzmA 38] ~~ [https://mp.weixin.qq.com/s/pWltNSFShhSzfGi_HQYVVw 39] ~~ [https://mp.weixin.qq.com/s/X1TM7K7Aq7QjSqQ7uMqIVA 40] ~~ [https://mp.weixin.qq.com/s/TKnIeV5DjTG4CVzS_x4sXQ 41] ~~ [https://mp.weixin.qq.com/s/jpQWt8b8L2YcRviW7jojOQ 42] ~~ [https://mp.weixin.qq.com/s/ln9IEv_ZLL3D_GT2v1nEOw 43] ~~ [https://mp.weixin.qq.com/s/T3pBKJvslZQmq-6mIWJQQQ 44] ~~ [https://mp.weixin.qq.com/s/1ulz0MMlu4cSKtrvjeA06w 45] ~~ [https://mp.weixin.qq.com/s/5qmo3P71oGuyhhfQ3zwTGA 46] ~~ [https://mp.weixin.qq.com/s/a2_r7xzWciEd2ktqvnryvA 47] ~~ [https://mp.weixin.qq.com/s/ouLTXKviUxBZ8zG12hG1SQ 48] ~~ [https://mp.weixin.qq.com/s/8n3pGkdYbg6pxTmr2IkT1g 49] ~~ [https://mp.weixin.qq.com/s/Sxe4Oufc4XeoWNR582qzew 50] ~~ [https://mp.weixin.qq.com/s/iMo_-Y0QmljBtAI7m-uQQA 51] ~~ [https://mp.weixin.qq.com/s/XtzFJuI_hYtrqEl4V87a4A 52] ~~ [https://mp.weixin.qq.com/s/lpl9epvVSw56jvmh2gO4zw 53] ~~ [https://mp.weixin.qq.com/s/gAHBgfBafPEL96bUHiZuHQ 54] ~~ [https://mp.weixin.qq.com/s/S5RoymKevsmDVU-h12OKGA 55] ~~ [https://mp.weixin.qq.com/s/aFjRb6larXn2_UbDTPv3ew 56] ~~ [https://mp.weixin.qq.com/s/TBTQLpVUawc1IqU8xgLY1Q 57] ~~ [https://mp.weixin.qq.com/s/IUgiZHXfaW48lydWLiobKQ 58] ~~ [https://mp.weixin.qq.com/s/GxP84KKtDdXlY7g0_0I6Mw 59] ~~ [https://mp.weixin.qq.com/s/X1GSj18vE0BIiRn1Cx2KtA 60] ~~ [https://mp.weixin.qq.com/s/4Xm7x3Ii9CSgyuzmXyPz7A 61] ~~ [https://mp.weixin.qq.com/s/ItBLUQIOzvgupxd3Id9RZA 62] ~~ [https://mp.weixin.qq.com/s/8fI-ZPTuKkGfF6R3QH3tbA 63] ~~ [https://mp.weixin.qq.com/s/f5OeBW244O-t-AJTQ8_PIQ 64] ~~ [https://mp.weixin.qq.com/s/qMQcEfkstYfL966c5oqujQ 65] ~~ [https://mp.weixin.qq.com/s/1yxZR6Wn2W8VD_ouG7tjGw 66] ~~ [https://mp.weixin.qq.com/s/8jreASliDp6l7LxyrdPytw 67] ~~ [https://mp.weixin.qq.com/s/88l17sBOsbk0sWUfIHUtIQ 68] ~~ [https://mp.weixin.qq.com/s/fjT3X4fSEDzzeC9nXIKd0w 69] ~~ [https://mp.weixin.qq.com/s/czaYIAZNMgDgLQJl1Ti-5A 70]
\n
- [https://mp.weixin.qq.com/s/L9JkpAoyyGjvCf_c9F2izg 71]
== Numerical Partial Differential Equations
- Finite Difference Method: ~ [https://mp.weixin.qq.com/s/2vWukkAhRTsWpNG0k39qcA 01] ~~ [https://mp.weixin.qq.com/s/8L9gSpBt2Ct3WJlLBWzXAA 02] ~~ [https://mp.weixin.qq.com/s/__DWloos1aaSCIQXolCTXQ 03] ~~ [https://mp.weixin.qq.com/s/zxeRfab6dt9q6E8T7__nAQ 04] ~~ [https://mp.weixin.qq.com/s/t9OloF8uFHeISuhHfiHBNQ 05] ~~ [https://mp.weixin.qq.com/s/o6c0tiYqGIdqL6orvmjzHA 06] ~~ [https://mp.weixin.qq.com/s/u9qustoE9BFc4XjIK_IFPg 07] ~~ [https://mp.weixin.qq.com/s/ap3vP8WPhpiM9YVHWULXcQ 08] ~~ [https://mp.weixin.qq.com/s/-slrlYFG2jlfayY5Qe8wWw 09] ~~ [https://mp.weixin.qq.com/s/30V-6x92PJneoZ9uolm4Mw 10]
- Finite Volume Method
- Finite Element Method
- Boundary Element Method
- Spectral Method
- Machine Learning-based Method: ~ [https://mp.weixin.qq.com/s/bL9YiMNXlm1vRjXkv_4LWQ 01] ~~ [https://mp.weixin.qq.com/s/ouE9ufBIzf0uqAKYmtDwFA 02] ~~ [https://mp.weixin.qq.com/s/wTSPE2nWtEGlJDHYQJpNXQ 03] ~~ [https://mp.weixin.qq.com/s/UDxs4WyT8Gu2DKegzwLGUw 04] ~~ [https://mp.weixin.qq.com/s/bf07htR2_6PlaS1H_Bsm0A 05] ~~ [https://mp.weixin.qq.com/s/3Wskk1tj103x2GWyPdpZDg 06]