Instability of The Quadratic Equation
For example, consider the venerable quadratic equation:
- ,
with the two exact solutions:
This formula may not always produce an accurate result. For example, when c is very small, loss of significance can occur in either of the root calculations, depending on the sign of b.
The case, will serve to illustrate the problem:
We have
In real arithmetic, the roots are
In 10-digit floating-point arithmetic,
Notice that the solution of greater magnitude is accurate to ten digits, but the first nonzero digit of the solution of lesser magnitude is wrong.
Because of the subtraction that occurs in the quadratic equation, it does not constitute a stable algorithm to calculate the two roots.
Read more about this topic: Loss Of Significance
Famous quotes containing the words instability of, instability and/or equation:
“What exacerbates the strain in the working class is the absence of money to pay for services they need, economic insecurity, poor daycare, and lack of dignity and boredom in each partner’s job. What exacerbates it in upper-middle class is the instability of paid help and the enormous demands of the career system in which both partners become willing believers. But the tug between traditional and egalitarian models of marriage runs from top to bottom of the class ladder.”
—Arlie Hochschild (20th century)
“Not only does the wind of accidents stir me according to its blowing, but I am also stirred and troubled by the instability of my attitude.”
—Michel de Montaigne (1533–1592)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)