CS1371 Introduction to Computing for Engineers

1
CS1371Introduction to Computing for Engineers

• Numerical Computing
• Interpolation

2
Administrivia

• Homework Now due Monday night (midnight)
  October 31 - BOOH!
• Exam WED NOV 2!!
• Through images (I am pretty sure!)
• Reading
• Numerical computing - Smith, Chapter 20

3
Trajectory through Computation

• Interpolation essentially curve fitting
• Integration and Differentiation
• Computing Solutions (not in book)
• Zeros
• bracketing
• Newton's (with care)
• Find Max
• Bracketing
• Fitting parabola OK when data is well behaved

4
Data Problems

• Real data is typically ugly
• Problem 1 Sparse only a few points
• Interpolation
• Not so smart NN, linear
• Splines real actual pieces of metals

5
Data interpolation

• x 0.54pi
• y sin(x) sin(2x)/2
• plot(x,y,'bo-') - shows linear
• Now assume have only the points, but not the
  function
• xx 0.14pi finer sampling
• yy interp1(x,y,xx)
• hold on
• plot(xx,yy,'r')
• zoom in looks the same! Interp1 does linear by
  default
• yyy interp1(x,y,xx,'spline')
• plot(xx,yyy,'b')
• ytrue sin(xx) sin(2xx)/2
• plot(xx,ytrue,'g')
• better, is it more accurate?
• doc interp1 and doc spline

6
More Problems

• Problem 2 Noisy Data
• Don't really want to exactly fit to the points
• Example miles per gallon
• Real question what is the "best fit"
• 'polyfit(x,y,n)' minimizes "squared error"
• n is "degree" of the polynomial
• Splines go through sparse data (knot points)
  curve fitting approximates data (handles noise)

7
Polyfit

• x 05
• fine_x 0.15
• y 0 20 60 68 77 110
• for order 25
• y2polyval(polyfit(x,y,order), fine_x)
• subplot(2,2,order-1)
• plot(x, y, 'o', fine_x, y2)
• axis(-1 7 -20 120)
• ttl sprintf('Degree d Polynomial Fit', order
  )
• title(ttl)
• xlabel('Time (sec)')
• ylabel('Temperature (degrees F)')
• end