intelligent numerical computation1 numerical analysis matlab programming numerical methods...

Intelligent Numerical Computation 1

Numerical Analysis

MATLAB programming Numerical Methods Applications

Contents


References:1. Numerical mathematics and computing, fourth Edition, Cheney&Kincaid, 19992. Lecture slides ftp://134.208.26.91 user:ndhu passwd:ndhu port:48103. G. Rechtenwald, Numerical methods with MATLAB: Implementation and application.

ftp://134.208.26.91/


A. Homework 30%

B. Midterm 30%

C Final Exam 40%

Grading


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


Locating roots of equations

Task:given a function f, find a solution x such that f(x)=0Related methods: Bisection method, Newton method, Secant method

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


Interpolation and numerical differentiation


Numerical integration:

Trapezoid rule, Simpson rule

system of linear equations

Ax=b

Approximation by spline functions:

natural cubic spline, B-splines


Smoothing and the least square method


Traveling salesman problems


Independent component analysis

0 20 40 60 80 100 120 140 160 180 200-2

0

2

0 20 40 60 80 100 120 140 160 180 200-2

0

2

0 20 40 60 80 100 120 140 160 180 200-2

0

2

0 20 40 60 80 100 120 140 160 180 200-2

0

2

0 20 40 60 80 100 120 140 160 180 200-2

0

2

Observations


Independent component analysis

0 20 40 60 80 100 120 140 160 180 200-2

0

2

0 20 40 60 80 100 120 140 160 180 200-2

0

2

0 20 40 60 80 100 120 140 160 180 200-2

0

2

0 20 40 60 80 100 120 140 160 180 200-2

0

2

0 20 40 60 80 100 120 140 160 180 200-2

0

2

Recovered sources


Classification- Face detection


Classification- Face recognition


FNA細胞樣本

A camera on a Microscope

Feature extractor

Breast CancerDiagnosis

BenignOr Malignant

Features:clump thicknessuniformity of cell sizeuniformity of cell shapemarginal adhesionsingle epithelial cell sizebare nucleibland chromatinnormal nucleoli and mitoses

Classification – breast cancer diagnosis


Blind source separation

music and speech


Blind source separation

music and speech

Blind Source separation


Blind source separation – fetal ECG

BSS


sources

mixed images

AemICA

JadeICA

Figure 10

Intelligent Numerical Computation 22Figure 11

Fz

Cz

Pz

Oz

C3

F4

F3N1 N2

P3

P2

Intelligent Numerical Computation 23Figure 12

Fz

Cz

Pz

Oz

C3

F4

F3

N1 N2P2

P3


x

x

x

xx

)(1,21 xG)(1,21 xG

)(1,21 xG

)(1,21 xG)(1,21 xG


a.

b.

)(7 zy

))(exp())(exp( 2,212,21 zz GG

)(7 zy

)(7 zy

))(exp( 2,21 zG

))(exp( 2,21 zG


)(zy

Function Approximation


Basic structure of a flowchart or a program

start

end

statements

Statements are executed one by oneA 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


Control statements

If statement

condition

statements

false

true

tag = 0; if ~ tag tag = tag+1;end


Control statements

If else statement

condition

statements

false or 0

true or 1

statements

if ~ tag tag = tag +1; else tag = tag –1; end


Control statements

for statement

statements

false

true

Example x=2; for i = 1:10 x = x*x; end

i =1

10i

i=i+1


Control statements

while statement

statements

false

true

Example

a=1; b=2; while a < 100 a = a*b; end

a<100


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

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