REVIEWER IN NUMERICAL ANALYSIS Numerical Analysis- deals with the process of getting the numerical solution to complex problems. To make a tough Mathematical problem easier to solve, an approximation is essential. Random Error - Due to natural fluctuations in measurement or computational systems. By definition, these fluctuations are random and therefore, the average random error is zero Systematic Error - A repeated “bias” in the measurement or computational system. -It is the study of algorithms that use numerical approximation to well defined mathematical problems For engineering applications, an approximation in the form of a rational number that is “close enough” is used instead of an irrational number. Babylonian Method: - Old method for getting the square root. - Once the two values are close, up to an acceptable level, we say that convergence has been achieved. Errors- associated with both calculations and measurements can be characterized by their accuracy and precision Accuracy – Measure of how closely a computed or measured value agrees with the true value. Precision - Measure of how closely individual computed or measured values agree with each other Degree of Precision - For measurement, the smallest value that can be measured or computed. 15 ±1mm For computational devices, - The algorithm of computation- The storage capacity - The number of stored digits Single Precision (6-9 significant digits) Double Precision (15-17 significant digits) Arbitrary Precision Taylor Series- is an expansion of some function into an infinite sum of terms