optimization.docx

# Figure 4 finding the coefficient figure 4 shows the

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algorithm and the computation of the divided difference table. Figure 4. Finding the coefficient Figure 4 shows the algorithm for finding the coefficient of the newton polynomial by assigning it as x0. Then we sum the coefficient to find the data function as a given point (IP=sum(c) ; ).

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25 Figure 5. Running the program After encoding the program, save and execute for simulation in the Scilab console. Figure 6. Results of program execution. This figure shows the Scilab console. In order to get the desired interpolation at a given point in a function of x, one must encode the datas of x and f, according to the table of heat and corresponding specific heat, based on the problem given. And also indicate the point of
26 interpolation as x0. Then call out the function IP and that will yield to the answer of the Newton’s Divided Difference of interpolation. Figure 7. Shows the Divided Difference Table and the yielded answer. Figure 8. Shows command to plot the data given.

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27 Figure 9. Plotted points of the data given, including the point of interpolation. Transcript of the program in the scinotes: funcprot(0) function IP =Newton_Divided ( x , f , x0 ) n=length( x ); a(1)= f (1); for k=1:n-1 D(k,1)=( f (k+1)- f (k))/( x (k+1)- x (k)); end
28 for j=2:n-1 for k=1:n-j D(k,j)=(D(k+1,j-1)-D(k,j-1))/( x (k+j)- x (k)) end end disp(D,'The Divided Difference Table') for j=2:n a(j)=D(1,j-1); end Df(1)=1; c(1)=a(1); for j=2:n Df(j)=( x0 - x (j-1))*Df(j-1) c(j)=a(j)*Df(j); end IP =sum(c); Endfunction Transcript of the program in the scilab console:

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29 x=[22 42 52 82 100] f=[4181 4179 4186 4199 4217] x0=90 IP=Newton_Divided(x,f,x0) VIII. Conclusion There are new and traditional ways to solve interpolation problems. With knowledge on manual calculations and basic programming skills using the Scilab application, we can come up with solutions for Newton’s Divided Difference problems. With the aid of Scilab, it is much easier to solve for algorithms and mathematical problems such as Newton’s Divided Difference and Optimization. With Scilab, solving can be easier, faster and efficient. References
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