Numerical Value
To calculate the numerical value of the natural logarithm of a number, the Taylor series expansion can be rewritten as:
To obtain a better rate of convergence, the following identity can be used.
- provided that y = (x−1)/(x+1) and x > 0.
For ln(x) where x > 1, the closer the value of x is to 1, the faster the rate of convergence. The identities associated with the logarithm can be leveraged to exploit this:
Such techniques were used before calculators, by referring to numerical tables and performing manipulations such as those above.
Read more about this topic: Natural Logarithm
Famous quotes containing the word numerical:
“The moment a mere numerical superiority by either states or voters in this country proceeds to ignore the needs and desires of the minority, and for their own selfish purpose or advancement, hamper or oppress that minority, or debar them in any way from equal privileges and equal rights—that moment will mark the failure of our constitutional system.”
—Franklin D. Roosevelt (1882–1945)
“The terrible tabulation of the French statists brings every piece of whim and humor to be reducible also to exact numerical ratios. If one man in twenty thousand, or in thirty thousand, eats shoes, or marries his grandmother, then, in every twenty thousand, or thirty thousand, is found one man who eats shoes, or marries his grandmother.”
—Ralph Waldo Emerson (1803–1882)