Numerical Methods: Approximation

Numerical methods serve to approximate solutions to mathematical equations and solve mathematical problems using computational power after algorithms have been developed. Methods exist for finding roots of polynomial equations for example or factoring matrices. Generally a convergence process if stable leads to the right result much like Taylor polynomials approximating the values of various functions where the Taylor polynomials act as a series progressing towards infinite.

Relevant concepts from calculus are the mean value theorem and the intermediate value theorem as well as Rolle’s theorem which all serve to answer how a bounded well-behaved function reflects its various properties in terms of itself. This is all analysis.

 

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