NUMERICAL METHODS

The field of numerical analysis predates the invention of modern computers by many centuries.Linear interpolation was already in use more than 2000 years ago.Many great mathematicians of the past were preoccupied by numerical analysis,as is obvious from the names of important algorithms like Newton's method,Lagrange interpolation polynomial,Gaussian elimination or Euler's method.

To facilitate computatios by hand ,large books were produced with formulas and tables of data such as interpolation points and function coefficients.Using these tables,often calculated out to 16 decimal places or more for some functions,one could look up values to plug into the formulas given and achieve very good numerical estimates of some functions.The canonical work in the field es the NIST publication edited by Abramowitz and stegun, a 1000-plus page bookof a very large numbre of commonly used formulas and functions and very useful when a computer is available, but the large listing of formulas can still be very handy.
The mechanical calculator was also developed as a tool for hand computation.These calculators evolved into electronic computers in the 1940's, and it was then found that these computers were also useful for administrative purposes.But the invention of the computers also influenced the field of numerical analysis, since now longer and more complicated calculations could be done.