numerical analysis
Sign in to savestudy of algorithms that use numerical approximation for the problems of mathematical analysis
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Numerical analysis is the study of methods and algorithms that solve mathematical problems by using approximate numbers rather than exact ones. It matters because many real-world mathematical problems are too complex to solve exactly, so these approximation techniques allow scientists, engineers, and others to get practical answers quickly.
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Babylonian clay tablet YBC 7289 (c. 1800–1600 BCE) with annotations. The approximation of the square root of 2 is four sexagesimal figures, which is about six decimal figures. 1 + 24/60 + 51/60 + 10/60 = 1.41421296... Numerical analysis is the study of algorithms for the problems of continuous mathematics. These algorithms involve real or complex variables (in contrast to discrete mathematics), and typically use numerical approximation in addition to symbolic manipulation.
Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.