Evaluating a polynomial can be an \"expensive\'\' thing for a computer. The \"ch

Question

Evaluating a polynomial can be an "expensive'' thing for a computer. The "cheapest'' way to evaluate a polynomial is to use a recur algorithm. For example, if p_4(x) = 3 - 2x + x^2 - 5x^3 + x^4, begin by rewrite it in a modified expanded form as follows: p_4(x) = 3 + x (-2 + x (1 + x (-5 + x))). Then p_4(x) - 3 + xp_3(x), where p_3(x) = -2 + xp_2(x), p_2(x) = 1 + xp_1(x), and P_1 (x) = -5 + x. To evaluate p_4(2) we calculate as follows: P_1(2) = -3 rightarrow P_2(2) = 1 + 2p_1(2) = -5 rightarrow fp_3(2)= -2 + 2p_2(2) = -12 rightarrow P_4(2) = 3 + 2p_3(2) = -21. Write a recourse Mat lab function called reapply to calculate the value of any polynomial function given a list of its coefficients (in ascending order) and a value of x. Program specifications and sample function calls are below. input parameter cleat a vector of coefficients in ascending order input parameter ins value(s) at which to evaluate the polynomial output parameter outs value(s) of the polynomial at ins Matlab has a built-in function called polygala which accomplishes the sun- job as your function reapply but you are forbidden to use it in your program. However. you may use it to your code: reapply(clast, ins) should produce the same value as the built-in Mat lab function polygala (flipper(clast) ins) for any value ins und any vector of coefficients clast.

Explanation / Answer

Matlab Code:

function outs = revalpoly(clist,ins)
for j=1:length(ins)
px0 = 1;
for i=length(clist):-1:2
if i==length(clist)%checks the first iteration
px = clist(i-1)+ins(j)*clist(i);
px0 = px;
else%checks the later iterations
px = clist(i-1)+ins(j)*px0;
px0 = px;
end
disp(px0);
end
outs(j)=px0;
end
end

Command window output:

>> revalpoly([3 -2 1 -5 1],[2 3])
-3

-5

-12

-21

-2

-5

-17

-48

ans =

-21 -48

>> polyval(fliplr([3 -2 1 -5 1]),3)

ans =

-48

>>

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