3) Let consider the following algorithm: Polynomial evaluation This algorithm evaluates the polynomial p(x) -Σ-0Ck xT Lk=0 n-k At the point t. Input: The sequence of coefficients co, C1, ..., Cn, the value t and n Output: p(t) Procedure poly(c, n, t) If n = 0 then Return (co) Return (t · poly(c, n-1, t) + Cn) End poly Let b, be the number of multiplications required to compute p(t). a) Find the recurrence relation and initial condition for the sequence {bn} b) Compute b1, b2 and b3. c) Solve the recurrence relation.

3) Let consider the following algorithm: Polynomial evaluation This algorithm evaluates the polynomial p(x) -Σ-0Ck xT Lk=0 n-k At the point t. Input: The sequence of coefficients co, C1, ..., Cn, the value t and n Output: p(t) Procedure poly(c, n, t) If n = 0 then Return (co) Return (t · poly(c, n-1, t) + Cn) End poly Let b, be the number of multiplications required to compute p(t). a) Find the recurrence relation and initial condition for the sequence {bn} b) Compute b1, b2 and b3. c) Solve the recurrence relation.

Name: discrete mathematics/structures 3) Let consider the following algorith
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Description: discrete mathematics/structures 3) Let consider the following algorithm: Polynomial evaluationThis algorithm evaluates the polynomialp(x) -Σ-0Ck xTLk=0n-kAt the point t.Input: The sequence of coefficients co, C1, ..., Cn, the value t and nOutput: p(t

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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discrete mathematics/structures

3) Let consider the following algorithm: Polynomial evaluation
This algorithm evaluates the polynomial
p(x) -Σ-0Ck xT
Lk=0
n-k
At the point t.
Input: The sequence of coefficients co, C1, ..., Cn, the value t and n
Output: p(t)
Procedure poly(c, n, t)
If n = 0 then
Return (co)
Return (t · poly(c, n-1, t) + Cn)
End poly
Let b, be the number of multiplications required to compute p(t).
a) Find the recurrence relation and initial condition for the sequence {bn}
b) Compute b1, b2 and b3.
c) Solve the recurrence relation.

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