Numerical Methods using MATLAB
Language: English
Pages: 137
ISBN: 1484201558
Format: PDF / Kindle (mobi) / ePub
Numerical Methods with MATLAB provides a highly-practical reference work to assist anyone working with numerical methods. A wide range of techniques are introduced, their merits discussed and fully working MATLAB code samples supplied to demonstrate how they can be coded and applied.
Numerical methods have wide applicability across many scientific, mathematical, and engineering disciplines and are most often employed in situations where working out an exact answer to the problem by another method is impractical.
Numerical Methods with MATLAB presents each topic in a concise and readable format to help you learn fast and effectively. It is not intended to be a reference work to the conceptual theory that underpins the numerical methods themselves. A wide range of reference works are readily available to supply this information. If, however, you want assistance in applying numerical methods then this is the book for you.
the path taken (e.g. its length, elevation and road conditions), the journey time (which defines the traffic), environmental conditions and vehicle or mode of transportation (for example, should I choose bus, car or bike? Sometimes it is faster to go by bike than by car for short distances if parking can cause delays). These parameters can be further dependent on/consist of other parameters, e.g. vehicle parameters consist of mileage, vehicle conditions, and so on. The parameters may also be
f=@(x) sin(x)-c/10; x(c+1)=fzero(f,[0 3.14]); end Defining Constraints If the optimization has constraints over parameters, then we need to select a built-in function written specifically for constrained optimization and define the constraints to pass them to the selected function. There are various types of constraints and each can be defined in the following way: Linear Constraints Linear constraints can be of two types 1.Equalities of the form A eq (x) = B eq . 2.Inequalities of
the system to collect samples of input and output signals. Then we try to find a relation between output and inputs with some basic assumptions about the system. Given any two data sets, the derivation of a relation is known as regression. In this chapter, we will first learn the basic concepts and methods of regression and then use this knowledge to perform model fitting. Regression Regression is a general term for any method which computes the relation between two or more data variables using
or function with the same name. This is also true for inbuilt functions. For example, we saw that sin is used to compute the sine of a variable. Let us define our own variable sin and then try to call the sin function sin=4; d=sin*3 y=sin(3); We will get d=12, but the next line will cause an error because sin is treated as a variable here and it is trying to access the third element of the sin matrix. Here, ( . ) denotes indexing, which we will learn more about later. To see this
Clipping a Signal Suppose a signal x(t) is given as t=0:.01:2*pi x=sin(2*pi*t); Suppose we apply this signal to a clipper circuit which can only pass a signal between -0.9 and 0.7. The following operation will generate the equivalent output y(t) y=x; y(y>0.7) = 0.7; y(y<-0.9) = -0.9; Halving a Matrix A=rand(100,100); B=A(1:2:end,1:2:end); Vectorization It should be clear by now that MATLAB is designed for vector and matrix operations. You can often speed up your M-file code