Assignment Degree Essay Example | Topics and Well Written Essays - 1000 words

Assignment Degree - Essay Example Numerical root-finding methods use iteration, producing a sequence of numbers that hopefully converge towards a limit (the so called "fixed point") which is a root. The first values of this series are initial guesses. The method computes subsequent values based on the old ones and the function f. The bisection method is based on the fact that a function will alter sign when it passes through zero. The bisection method can halve the size of the interval in each iteration and eventually find the root by evaluating the function at the middle of an interval and replacing whichever limit has the same sign. False position method is an algorithm of the prior estimate for which the function value has opposite sign from the function value at the current best estimate of the root. In this method, the root is bracketed. Similar to the secant method, the false position method also uses a straight line to approximate the function in the local region of interest. The secant method is based on the assumption that the function is approximately linear in the local region of interest and uses the zero-crossing of the line connecting the limits of the interval as the new reference point. The next iteration starts from evaluation of the function at the new reference point, and then it forms another line. The process is repeated up to the time of finding root. The Newton-Raphson method finds the slope (the tangent line) of the function at the current ... The process is repeated until the root is found. 5. Fixed Point Iteration: It is a method of computing fixed points of iterated functions. For example, given that a function f defined on the real numbers having real values and given a point x0 in the domain of f, the fixed point iteration is which gives rise to the sequence which is hoped to converge to a point x. If f is continuous, then one can prove that the obtained x is a fixed point of f, i.e., f(x) = x. 6. Muller's Method: Muller's method is generalized from the secant method, in the sense that it does not require the derivative of the function. It is an iterative method that needs three starting points, , and .A parabola is constructed that passes through the three points; then the quadratic formula is used to find a root of the quadratic for the next approximation.The following equation generalizes the secant method of root finding by using quadratic 3-point interpolation : Then the following is defined : (2) (3) (5) The next iteration is described by this equation: Source : Abramowitz, M. and Stegun, I.A. (Eds). Handbook of Mathematical Functions with formulas, Graphs, and Mathematical Tables, 9th

Statistics for Managers Individual Work wk3 Essay

Statistics for Managers Individual Work wk3 - Essay Example For instance, an automobile industry can analyze the likelihood of a parts failure in an automobile. Discrete random variable is delineated as a variable in which all the outcomes cannot be broken into smaller measurements and are also mutually exclusive. It exists on either infinitely or finitely countable continuum. Continuous random variable is delineated as infinitely unaccountable probability space. Despite the fact that each event is peculiar, it is not possible to measure the probability of a single event given that it can be further divided into smaller parts. (Lind, & Mason, 2000) This is a random variable because its value is determined by chance, and is unknown in future. An analysis of discrete random variables will be utilized in a supply industry company in which defects can be measured via 100 invoices. This sample size allows discrete random variables as. In addition, process mapping allows multiple phases of data analysis to have visual work force. The possible values this random variable can assume are the values of each card in the deck: two, three, four, and so on. Because these values are distinct, indivisible amounts, the random variable is discrete. This helps balance customer gaps and assure quality assurance to the highest degree. This information can be assessed to use as data to trigger sales in every department. An analysis of continuous random variables is measuring the time with customers coming and entering the retail at a specific time. Continuous random variables can be utilized in Wal-Mart in which customers are coming in 3 minutes 32 seconds of 5 minutes 17.6 seconds. This is crucial to quantify the data in essence to have a visual display of the work that is being conducted. For instance, suppliers and vendors can look at this data to analyze when customers are coming at the right time. Inputs can be utilized to include process activity in which customers