MTH 221 - Discrete Math for Information Technology

Nov 27th, 2013
Anonymous
Category:
Art Design
Price: \$10 USD

Question description

Exercise 5.2, problems 27(a & b); p 259
One version of Ackermann’s function A(m,n) is defined recursively for m, n ∈ N by:

A(0, n)= n + 1, n ≥ 0;
A(m, 0) = A(m − 1, 1), m > 0; and
A(m, n) = A(m − 1, A(m, n − 1)), m, n > 0.

a. Calculate A(1, 3) and A(2, 3).
b. Prove that A(1, n) =  n + 2 for all n ∈ N.
c. For all n ∈ N show that A(2, n) = 3 + 2n
d. Verify that A(3, n) =  2n+3 − 3 for all n ∈ N.

Exercise 5.8, problem 6; p 301 (take a look at problem 5 first)
We first note how the polynomial in Exercise 5 can be written in the nested multiplication method:

8 + x(−10 + x(7 + x(−2 + x(3 + 12x)))).

Using this representation, the following pseudocode procedure (implementing Horner’s method) can be used to evaluate the given polynomial.

procedure PolynomialEvaluation2
(n: nonnegative integer;
r,a0,a1,a2,. . .,an: real)
begin
value := an
for j := n - 1 down to 0 do
value := aj + r * value
end

a. How many additions take place in the evaluation of the given polynomial? (Do not include the n − 1 additions needed to increment the loop variable i.) How many multiplications?
b. Answer the questions in part (a) for the general polynomial a0 + a1x + a2x2 + a3x3 + · · · + an−1xn−1 + anxn, where a0, a1, a2, a3, . . . , an−1, an are real numbers and n is a positive integer.

(Top Tutor) Yasir001
School: University of Virginia

Studypool has helped 1,244,100 students

Review from student
Anonymous
" Totally impressed with results!! :-) "

1819 tutors are online

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors