Intelligent Numerical Computation1 Numerical Analysis MATLAB programming Numerical Methods Applications Contents

Intelligent Numerical Computation2 References: 1. Numerical mathematics and computing, fourth Edition, Cheney&Kincaid, Lecture slides ftp:// user:ndhu passwd:ndhu port:4810ftp:// G. Rechtenwald, Numerical methods with MATLAB: Implementation and application.

Intelligent Numerical Computation3 A. Homework 30% B. Midterm 30% C Final Exam 40% Grading

Intelligent Numerical Computation4 Numerical Methods I  Locating roots  Interpolation and numerical differentiation  Numerical integration  Solving a system of linear equations  Approximation by spline functions  Smoothing and the least-square method

Intelligent Numerical Computation5 Locating roots of equations Task:given a function f, find a solution x such that f(x)=0 Related methods: Bisection method, Newton method, Secant method

Intelligent Numerical Computation6 Interpolation and numerical differentiation

Intelligent Numerical Computation7 Interpolation and numerical differentiation

Intelligent Numerical Computation8  Numerical integration: Trapezoid rule, Simpson rule  system of linear equations Ax=b  Approximation by spline functions: natural cubic spline, B-splines

Intelligent Numerical Computation9 Smoothing and the least square method

Intelligent Numerical Computation10 Traveling salesman problems

Intelligent Numerical Computation11 Independent component analysis Observations

Intelligent Numerical Computation12 Independent component analysis Recovered sources

Intelligent Numerical Computation13 Classification- Face detection

Intelligent Numerical Computation14 Classification- Face detection

Intelligent Numerical Computation15 Classification- Face detection

Intelligent Numerical Computation16 Classification- Face recognition

Intelligent Numerical Computation17 FNA 細胞樣本 A camera on a Microscope Feature extractor Breast Cancer Diagnosis Benign Or Malignant Features: clump thickness uniformity of cell size uniformity of cell shape marginal adhesion single epithelial cell size bare nuclei bland chromatin normal nucleoli and mitoses Classification – breast cancer diagnosis

Intelligent Numerical Computation18 Blind source separation music and speech

Intelligent Numerical Computation19 Blind source separation music and speech Blind Source separation

Intelligent Numerical Computation20 Blind source separation – fetal ECG BSS

Intelligent Numerical Computation21 sources mixed images AemICA JadeICA Figure 10

Intelligent Numerical Computation22 Figure 11 Fz Cz Pz Oz C3 F4 F3 N1N2 P3 P2

Intelligent Numerical Computation23 Figure 12 Fz Cz Pz Oz C3 F4 F3 N1N2 P2 P3

Intelligent Numerical Computation24

Intelligent Numerical Computation25 a. b.

Intelligent Numerical Computation26 Function Approximation

Intelligent Numerical Computation27 Basic structure of a flowchart or a program start end statements Statements are executed one by one A statement can be an assignment: A = B*C-D : x = sort(x) a function for I/O : plot(x,y) : imread(X) a control statement -- if statement -- if else statement -- for statement -- while statement

Intelligent Numerical Computation28 Control statements If statement condition statements false true tag = 0; if ~ tag tag = tag+1; end

Intelligent Numerical Computation29 Control statements If else statement condition statements false or 0 true or 1 statements if ~ tag tag = tag +1; else tag = tag –1; end

Intelligent Numerical Computation30 Control statements for statement statements false true Example x=2; for i = 1:10 x = x*x; end i =1 i=i+1

Intelligent Numerical Computation31 Control statements while statement statements false true Example a=1; b=2; while a < 100 a = a*b; end a<100

Intelligent Numerical Computation32  Input your data, including texts, images, and sounds  Output: 2D plots & output messages  Basic control: if, for, while statements  Matrix manipulations  Function call  Speeding-up programs  Coding a method  Solving a problem MATLAB Programming