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Bagian 5 Beberapa Problem Optimasi : Curve Fitting

Metode Komputasi. Bagian 5 Beberapa Problem Optimasi : Curve Fitting. This is a file from the  Wikimedia Commons. Dosen :. Deni Saepudin : Ruang C114 Telp . +628122086193. Curve Fitting.

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Bagian 5 Beberapa Problem Optimasi : Curve Fitting

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  1. MetodeKomputasi Bagian5 Beberapa Problem Optimasi: Curve Fitting This is a file from the Wikimedia Commons. Dosen: DeniSaepudin : Ruang C114 Telp. +628122086193

  2. Curve Fitting • Merupakan proses membangunkurvaataufungsimatematika yang paling cocok (best fit) denganbarisan data point. • Curve fitting dapatberupa: • interpolasi (kecocokandengan data dituntutmutlak), • smoothing (fungsi yang digunakanharus smooth) dan • regressi (kecocokandengan data mengakomodasi random error)

  3. Ilustrasi: Model PenjualanRumah http://people.hofstra.edu/stefan_waner/realworld/calctopic1/regression.html Penyederhanaan

  4. Linear Curve Fitting Bilajumlahpenjualandiasumsikanbergantung linear terhadapharga Y = 1x + 0, x menyatakanharga Y menyatakanjumlahpenjualan Bagaimanamenaksir parameter 1dan0? Definisi: Jarakvertikal Jarakvertikalantaragaris Y = 1x + 0ketitik Pi(xi, yi) ei = |yi – (1xi + 0)| = |yi – 1xi –0 | Garis Y = 1x + 0dipilihsehinggajumlahkuadratjarakvertikalterkecil

  5. Linear Least Square • Alternatif 1: MetodeKalkulus • Alternatif 2 : Metode Gradient Descent • Terapkanmetode Gradient descent utk problem tsb! Gariskuadratterkecil Y = 1x + 0untukhimpunantitik (x1,y1), (x2,y2),…,(xn,yn) dapatdiperolehdarimasalahpeminimuman Bagaimanamenentukannilai1dan0yang memenuhimasalahoptimasi?

  6. Nonlinear Fitting (linearisasi) Contoh: Data Penjualankomputercompaq Diberikansekumpulan data: (x1,y1),(x2,y2),…,(xn,yn) Jikahubunganantara Y dan X diasumsikan Y = eX, dapatdilakukanlinearisasi lnY = ln  +X (linearisasi) Maka Ytopi = lnY 0 = ln  1 = 

  7. Latihan: • Carilah model keuntunganpenjualankomputerberdasarkan data penjualankomputer Compaq • Gunakanasumsibahwamodelnyaeksponesial • Buat plot data empirikdan model yang diperolehdalamsatugambar

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