Why do we study approximation?

Approximation algorithms solve optimization problems, and provide a guaranteed bound on how close they get to the true optimum.

What is the purpose of approximation algorithm?

In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one.

Why do we need approximation algorithms How do we characterize approximation algorithms?

An approximation algorithm is a way of dealing with NP-completeness for an optimization problem. The goal of the approximation algorithm is to come close as much as possible to the optimal solution in polynomial time.

Why approximation is necessary when numerical analysis is used?

Even when solving finite systems of linear equations by direct numerical methods, infinite precision arithmetic is needed in order to find a particular exact solution. When approximating a problem, a numerical analyst would want to understand the behaviour of the error in the computed solution.

What is approximation algorithm Quora?

Approximation algos are used to find approximate solutions to optimization problems. This technique does not guarantee the best solution. It is often associated with NP hard problems. For detailed answer, you can get lot of information from the web. 1.5K views.

What is significance of approximation ratio in approximation algorithms?

Intuitively, the approximation ratio measures how bad the approximate solution is distinguished with the optimal solution. A large (small) approximation ratio measures the solution is much worse than (more or less the same as) an optimal solution.

What is approximation ratio give an approximation algorithm for Travelling salesman problem?

What is the 2 approximation algorithm for TSP? When the cost function satisfies the triangle inequality, we may design an approximate algorithm for the Travelling Salesman Problem that returns a tour whose cost is never more than twice the cost of an optimal tour. The idea is to use Minimum Spanning Tree (MST).

What is approximation numerical analysis?

The second type of numerical method approximates the equation of interest, usually by approximating the derivatives or integrals in the equation. The approximating equation has a solution at a discrete set of points, and this solution approximates that of the original equation.

What is the importance of numerical methods in computer science?

In addition, the purpose of most numerical analysis research is to develop actual computer codes to solve real problems; and thus the development of computer software to implement numerical algorithms is an important part of the subject.