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Introduction of Numerical Analysis

The study of algorithms that uses numerical estimation for the problems of mathematical analysis is termed as Numerical Analysis.

 

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One of the initial 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. Which is being capable to evaluate the sides of a triangle (and being capable to evaluate square roots) is extremely significant, for illustration, in carpentry and construction.

The numerical analysis continues this long custom of practical mathematical calculations. Much similar to the Babylonian approximation of the modern numerical analysis does not seek accurate answers, as accurate answers are frequently not possible to acquire in practice. Rather than that, much of numerical analysis is concerned with acquiring approximate results while maintaining the reasonable bounds on errors.

 

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Numerical analysis logically finds applications in every field of the physical sciences and the engineering, however in the 21st century, the life sciences and even the arts have adopted elements of scientific calculations. Common differential equations emerge in the movement of heavenly bodies (i.e., planets, stars and galaxies); optimization takes place in portfolio management; numerical linear algebra is significant for data analysis; stochastic differential equations and Markov chains are necessary in simulating living cells for medicine and biology.

Before the entrance of modern computers numerical methods frequently depended on hand interpolation in large printed tables. In the mid 20th century, rather than that the computers compute the needed functions. These similar interpolation formulas nevertheless continue to be used as a part of the software algorithms for solving differential equations.

The overall aim of the numerical analysis is the analysis and design of methods to give estimated but precise solutions to hard problems, the variety of which is recommended by the following.

  • Advanced numerical techniques are significant in making numerical weather prediction feasible.
  • Calculating the trajectory of a spacecraft need the precise numerical solution of a system of ordinary differential equations.
  • Car companies can improve the crash safety of their vehicles by the use of computer simulations of car crashes. This kind of simulations necessarily consists of solving partial differential equations numerically.
  • The private investment funds use tools from all fields of numerical analysis to compute the value of stocks and derivatives more exactly than the other market participants.
  • The Airlines use sophisticated optimization algorithms to decide the ticket prices airplane and crew assignments and fuel requirements. In the past, such algorithms were developed within the overlapping field of the operations research.
  • The Insurance companies use numerical program for the actuarial analysis.

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