Algorithms have been used to solve real-world problems since as far back as 1650 B.C., according to the University of Iowa. Archimedes of Syracuse developed a method for finding the areas, lengths and volumes of geometric figures. Isaac Newton and Gottfried Leibnitz created calculus, which allowed scientists to create accurate mathematical models of the physical world. These models were adapted to solve mathematical problems in engineering, business and medicine.
Numerical analysis is often used to solve systems of linear and nonlinear equations that often contain a large number of variables, according to the University of Iowa. Most linear systems are written in matrix-vector notation (Ax=b). "A" is the matrix of coefficients for the system, "x" represent the column vector for the unknown variables, and "b" is a given column vector. Nonlinear systems are solved through a series of linear equations.
The majority of numerical computation is done on digital computers now, according to the University of Iowa. This hardware shapes the properties and structure of numerical algorithms. Arithmetical methods varied greatly from one computer to next when computer science was first developed, according to the University of Iowa. This made transferring numerical data from one computer to another very difficult. The Institute for Electrical and Electronic Engineering (IEEE) developed a standard for floating-point arithmetic on computers, which has greatly lessened problems in transferring data.
Numerical analysts concern themselves with many different aspects of the numerical solution of problems. Each analyst is focused on a certain aspect, but all analysts have some methods, concerns and perspectives in common, according to the University of Iowa. Numerical analysts will often find problems similar to the ones they can't solve, in hopes that they can infer information from the similar problem's solution. Error is a huge concern for these analysts. Its analytic form and size are taken into consideration when solving any problem. Solved problems are scrutinized by slightly changing data to make sure finding the solution stays the same. All algorithms are measured for efficiency to be sure they can be applied to other sciences.
Numerical analysis has become crucial to many parts of modern life, according to the University of Iowa. Numerical analysis software has become part of many popular computer programs, such as those using spreadsheets. This analysis is uses in computer aided design (CAD), study of Earth's atmosphere and businesses' allocation of resources.