Computer Science: An Overview (12th Edition)
12th Edition
ISBN: 9780133760064
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
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Chapter 12.5, Problem 2QE
Program Plan Intro
Complexity of problems:
Whether the practical solution of any solvable problem is complex or not is investigated by the solvability of problems. Some problems that are theoretically solvable are so complex means from a practical point of view they are unsolvable called as complexity of problems.
The step by step instructions that are written in an organized manner to solve a problem in computer science is called algorithm.
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Jacobi method is an iterative algorithm for determining the
solutions of a strictly diagonally dominant system of linear
equations. Each diagonal element is solved for, and an
approximate value is plugged in. The process is then iterated until it
converges.
Further details of the method can be found at Jacobi Method with a
formal algorithm and examples of solving a system of 2/3 linear
equations. This also includes a python implementation of the
algorithm using numpy. But, in this assignment, you are required to
write python implementation using list/nested list data structure
without using any of the built-in python libraries for matrix
operations.
Write a python function Jacobi(A, b, x_init) where A is a
diagonal dominant matrix, b is list of constants (right-hand side of
the equations), and x_init (a list) is an initial guess to the
solution. The function returns the solution as a list (each value of
the list is rounded off to two decimal places).
>>> Jacobi([[2, 1, 1], [0, 2, 1],…
2. Algorithm A has a running time described by the recurrence T(n) = 7T(n/2) + n². A
competing algorithm B has a running time described by the recurrence T(n) =
aT (n/4) + n². What is the largest integer value for a such that B is asymptotically faster
than A? Explain your answer.
Show Let f(.) be a computable, strictly monotonic function, that is, f(n+ 1) > f(n) for all n. Show B = {f(n) | n ∈ N} is recursive.
Chapter 12 Solutions
Computer Science: An Overview (12th Edition)
Ch. 12.1 - Prob. 1QECh. 12.1 - Prob. 2QECh. 12.1 - Prob. 3QECh. 12.1 - Prob. 4QECh. 12.2 - Prob. 1QECh. 12.2 - Prob. 2QECh. 12.2 - Prob. 3QECh. 12.2 - Prob. 4QECh. 12.2 - Prob. 5QECh. 12.3 - Prob. 1QE
Ch. 12.3 - Prob. 3QECh. 12.3 - Prob. 5QECh. 12.3 - Prob. 6QECh. 12.4 - Prob. 1QECh. 12.4 - Prob. 2QECh. 12.4 - Prob. 3QECh. 12.5 - Prob. 1QECh. 12.5 - Prob. 2QECh. 12.5 - Prob. 4QECh. 12.5 - Prob. 5QECh. 12.6 - Prob. 1QECh. 12.6 - Prob. 2QECh. 12.6 - Prob. 3QECh. 12.6 - Prob. 4QECh. 12 - Prob. 1CRPCh. 12 - Prob. 2CRPCh. 12 - Prob. 3CRPCh. 12 - In each of the following cases, write a program...Ch. 12 - Prob. 5CRPCh. 12 - Describe the function computed by the following...Ch. 12 - Describe the function computed by the following...Ch. 12 - Write a Bare Bones program that computes the...Ch. 12 - Prob. 9CRPCh. 12 - In this chapter we saw how the statement copy...Ch. 12 - Prob. 11CRPCh. 12 - Prob. 12CRPCh. 12 - Prob. 13CRPCh. 12 - Prob. 14CRPCh. 12 - Prob. 15CRPCh. 12 - Prob. 16CRPCh. 12 - Prob. 17CRPCh. 12 - Prob. 18CRPCh. 12 - Prob. 19CRPCh. 12 - Analyze the validity of the following pair of...Ch. 12 - Analyze the validity of the statement The cook on...Ch. 12 - Suppose you were in a country where each person...Ch. 12 - Prob. 23CRPCh. 12 - Prob. 24CRPCh. 12 - Suppose you needed to find out if anyone in a...Ch. 12 - Prob. 26CRPCh. 12 - Prob. 27CRPCh. 12 - Prob. 28CRPCh. 12 - Prob. 29CRPCh. 12 - Prob. 30CRPCh. 12 - Prob. 31CRPCh. 12 - Suppose a lottery is based on correctly picking...Ch. 12 - Is the following algorithm deterministic? Explain...Ch. 12 - Prob. 34CRPCh. 12 - Prob. 35CRPCh. 12 - Does the following algorithm have a polynomial or...Ch. 12 - Prob. 37CRPCh. 12 - Summarize the distinction between stating that a...Ch. 12 - Prob. 39CRPCh. 12 - Prob. 40CRPCh. 12 - Prob. 41CRPCh. 12 - Prob. 42CRPCh. 12 - Prob. 43CRPCh. 12 - Prob. 44CRPCh. 12 - Prob. 46CRPCh. 12 - Prob. 48CRPCh. 12 - Prob. 49CRPCh. 12 - Prob. 50CRPCh. 12 - Prob. 51CRPCh. 12 - Prob. 52CRPCh. 12 - Prob. 1SICh. 12 - Prob. 2SICh. 12 - Prob. 3SICh. 12 - Prob. 4SICh. 12 - Prob. 5SICh. 12 - Prob. 6SICh. 12 - Prob. 7SICh. 12 - Prob. 8SI
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