Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian Collection (YBC 7289), which gives a sexagesimal numerical approximation of, the length of the diagonal in a unit square. Being able to compute the sides of a triangle (and hence, being able to compute square roots) is extremely important, for instance, in carpentry and construction.
Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of, modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors.
Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences and even the arts have adopted elements of scientific computations. Ordinary differential equations appear in the movement of heavenly bodies (planets, stars and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.
Before the advent of modern computers numerical methods often depended on hand interpolation in large printed tables. Since the mid 20th century, computers calculate the required functions instead. These same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations.
Read more about Numerical Analysis: General Introduction, Generation and Propagation of Errors, Areas of Study, Software
Famous quotes containing the words numerical and/or analysis:
“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)
“Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
—Octavio Paz (b. 1914)