eq-502 curve fitting - 3 constants data linear is at ion

8/14/2019 EQ-502 Curve Fitting - 3 Constants Data Linear is at Ion

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Data Linearisation of a curve defined by 3 constants

Select the sheet containing the order of polynomial to be fitted.

n ro uc on:Welcome to Computer Aided Analysis excel package.Using this applicatio

the following problems quickly.Curve fitting(3 constants)-This will solve the curve fitting problem of 3

detailed informationyou can seek help which is available at every sheet.

Important Notes:1.Every input is to be given in pink cells

2.The results are to be shown in various colors to your clear visibility.So at anyany values in cells other than pink cells

3.In every page there will be red color circle which guide you through step bycalculation

2cxbxay ++=

c

bxay+=

cxbeay +=


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Next

we could solve

onstants.For

ost do not input

tep progress of


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Input values: Data for fitting the curvea = 6 x y

b = 2 -2 22

c = 5 0.25 6.81

xmin = -2 2.5 42.25

xmax = 4 4.75 128.31

7 265

dx= 2.25

SolutionX Y X^2 XY

-1.75 -6.75 3.06 11.81

0.5 4.5 0.25 2.25

2.75 15.75 7.56 43.31

5 27 25 135 6.5 40.5 35.88 192.38

Normal Equation Solution4 6.5 b = 40.5 a = -6.00

6.5 35.88 c 192.38 b 2.00

c 5.00

Curve fitting of a polynomi

5

10

15

20

25

30

y

1

2

3

4 5


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l defined by y=a+bx+cx2Back Next Help

-4 -2 0 2 4 6 8

0

0

0

0

0

0

0

x

6
http://opt/scribd/conversion/tmp/scratch2347/http://opt/scribd/conversion/tmp/scratch2347/


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In this

Here us


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color bo

In the ta

writ

The tit

Back


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HELPsection we fit the two degree polynomial y=a+bx+cx2 and it is reduced to linear & one

degree polynomialas Y=AX+B.So the values,Y=(yi-y

1/xi-x

1);X=xi+x

1;A=c;B=b;a=bx

1+cx

12

r will be prompted to give constant values a,b,c and Xmin and Xmax as inputs only in the


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xes.The table 1 has some calculated data for input values i.e.y values corresponding to xvalues.

le 2 the actual two degree polynomial is assumed to be linear & one degree pol. Y=AX+Band those are

ten as functions of x,y,a,b,c.Then after all the corresponding values like X,Y,X2,XY arecalculated and tabulated here.

le Normal Equation has matrix format of equation which is going to be solved for 'b' and'c'.And finally

the solution title shows you that values 'a' ,'b' & 'c'.

Main M


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nu


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b = 1 1 2

c = 2 2 5xmin = 1 4 17

xmax = 16 8 65

16 257

a0 = 1

r = 2.00

SolutionX Y X^2 XY

0 0 0 0

0.69 1.39 0.48 0.96

1.39 2.77 1.92 3.84

2.08 4.16 4.32 8.652.77 5.55 7.69 15.37

6.93 13.86 14.41 28.83

Normal Equation

5 6.93 A = 13.86

6.93 14.41 B 28.83

Solution

A = 0.00 a = 1.00

B 2.00 b 1.00

c 2.00

Curve fitting of a polynomi

0 2

0

50

100

150

200

250

300

y

1

2

3

4

5


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l defined by y=a+bxc Back Next Help

4 6 8 10 12 14 16 18

Fitting Polynomial : y=a+bxc

x

6


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In this section we fit the pas Y=AX+B.So the v

Here user will be prompte

color boxes.The table 1 h

In the table 2 the actual p

written as functions o

The title Normal Equatio

the

Back


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HELPlynomial y=a+bxc and it is reduced to linear & one degree polynomial

alues,Y = log (yi-a);X = log xi;A=log b;B=c;a=(y2

2-y1y

3)/(2y

2-y

1-y

3)

to give constant values a,b,c and Xmin and Xmax as inputs only in therelevent pink

s some calculated data for input values i.e.y values corresponding to xvalues.

lynomial is assumed to be linear & one degree pol. Y=AX+B and thoseare

x,y,a,b,c.Then after all the corresponding values like X,Y,X2,XY arecalculated and tabulated here.

has matrix format of equation which is going to be solved for 'A' and'B'.And finally

solution title shows you that values 'a' ,'b' & 'c'.

Main Menu


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b = 1 1 20.09c = 3 3 8103.08

xmin = 1 5 ###

xmax = 9 7 ###

9 ###

d = 2

Solution

X Y XY

1 3 1 3

3 9 9 27

5 15 25 757 21 49 147

9 27 81 243

25 75 165 495

Normal Equation

5 25 A = 75

25 165 B 495

Solution

A = 0.00 a = 0.00

B 3.00 b 1.00

c 3.00

Curve fitting of a polyno

X2

0

0

50

100

150

200

250

300

y

1

2

3

4

5


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mial defined by y=a+becx Back Help

2 4 6 8 10 12 14 16 18

Fitting Polynomial:y=a+becx

x


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HELPIn this section we fit the polynomial y=a+becx and it is reduced to linear & one degree pol

as Y=AX+B.So the values,Y=log(yi-a);X=xi;A=log b;B=c;a=(y

22-y

1y

3)/(2y

2-y

1-y

3)

Here user will be prompted to give constant values a,b,c and Xmin and Xmax as inputs onrelevent pink

color boxes.The table 1 has some calculated data for input values i.e.y values corresponvalues.

In the table 2 the actual two degree polynomial is assumed to be linear & one degree pol.and those are

written as functions of x,y,a,b,c.Then after all the corresponding values like X,Y,X2,XYcalculated and tabulated here.

The title Normal Equation has matrix format of equation which is going to be solved for ''B'.And finally

the solution title shows you that values 'a' ,'b' & 'c'.

Back


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nomial

ly in the

ing to x

Y=AX+B

are

A' and

Main Menu

eq-502 curve fitting - 3 constants data linear is at ion

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