Pre-Engineering 220 Introduction to MatLab ® & Scientific Programming j kiefer
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- 2. Curve Fitting Interpolation
MatLab® Sidelight Number One1. Polynomialsa. Representation In MatLab®, polynomials are represented by a vector composed of the coefficients. Thusly, 
b. Evaluate A polynomial is evaluated using the command polyval. If p is the vector of coefficients and x is the argument, polyval(p,x) or y=polyval(p,x) The roots command gives the roots of a polynomial, as elements of a vector. r=roots(p) If the roots of a polynomial are known, then the coefficient vector can be obtained by the poly command. p=poly(r) c. Add, multiply, & divide Polynomials are added by adding the vectors of their coefficients. The shorter vector has to be padded with zeros to make the two vectors the same length. Multiplication of two polynomials is done with the conv command. c(x) = a(x) * b(x) c = conv(a,b) Division is done with the deconv command. u(x)/v(x) = q(x) + r(x) [q,r] = deconv(u,v) d. derivatives  k = polyder(p)
 k=polyder(a,b)
 [n m] = polyder(u,v) followed by [k,r] = deconv(n,m)
2. Curve Fitting & InterpolationMatLab® fits data to a polynomial using the least squares method. Fitting an nth degree polynomial to a table of (x,y) points. If the number of data points is m, then n must be m-1 or less, and greater than 0.
In the Tools menu of the Figure Window is a Basic Fitting tool. This can be used to fit a function to data interactively. See section 8.4 in the text. c. Interpolation MatLab® has four interpolating techniques built-in. The command is interpl. It estimates yi = f(xi), given a set of {x,y}. yi = interpl(x,y,xi,’method’) The methods available are ‘nearest’ returns the value of the nearest data point ‘linear’ carries out linear interpolation ‘spline’ carries out interpolation using a cubic polynomial based on the data points surrounding the interpolated point ‘pchip’ carries out interpolation using a cubic Hermite polynomial. Directory: physics physics -> Photometer and Optical Link Sensitivity issues, needs editing 1/2010 Purpose physics -> Photometer and Optical Link Purpose physics -> - physics -> Teacher Notes – Activity 14: Momentum in Collisions physics -> Teacher Notes – Activity 15: Impulse and Change in Momentum physics -> Linear Momentum Definition Download 8.69 Mb. Share with your friends:
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