numerical-methods-quadraticequation-exercise

This exercise is related to computer arithmetic:

Computer Arithmetic / Machine Precision (1): Quadratic Equation Solver

1. Implement a class that implements the interface QuadraticEquation of the package info.quantlab.numericalmethods.lecture.computerarithmetics.quadraticequation.

Important: The interface you have to implement is not part of this project. It is imported from another project that is referenced by this project. To have a look at this interface, you can select "Open Declaration" in your IDE (right-click on the interface name) or look here: https://github.com/qntlb/numerical-methods-lecture/blob/master/src/main/java/info/quantlab/numericalmethods/lecture/computerarithmetics/quadraticequation/QuadraticEquation.java

The class implementing QuadraticEquation should allow to solve the equation x^2 + p x + q = 0, finding the smallest root of this equation in a numerically stable way.

Note: As your task is to implement the interface, read the JavaDoc of that interface for a specification of what to do.

2. When done with 1) implement the method createQuadraticEquation of the class QuadraticEquationAssignmentSolution, such that it allows to create an object of the class you have implemented in 1).

A class like QuadraticEquationAssignmentSolution is called a Factory, because it allows to create objects. It allows us to create an object of your class, without knowing the name of your class. We will use this method to test your implementation.

Hint: This is a trivial task. If your class in 1) is named QuadraticEquationFromCoefficients and if it has a constructor QuadraticEquationFromCoefficients(q,p), then the body of the implementation of the factory class is just

  public QuadraticEquation createQuadraticEquation(double q, double p) {
    return new QuadraticEquationFromCoefficients(q,p);
  }

You can test your implementation by running the unit test in src/test/java.

Main Task

The main task of this exercise is to provide a numerically stable formula implementation of the method getSmallestRoot.

Depending on the value of the coefficients q and p of the quadratic equation, the well known formulas for the root of the quadratic equation may exhibit large cancellation errors.