Matematiska vetenskaper, Chalmers Tekniska Högskola och Göteborgs Universitet

[hem, vecka 1, vecka 2, vecka 3, vecka 4, vecka 5, vecka 6, vecka 7]

ALA-A, studio4.1, 2006

The bisection algorithm 2.

1. Write a program for the bisection algorithm according to the template bisectdemo.m and this flowchart.

2. Use the program on some of the following equations.

(a) x2=2

(b) x4=2

(c) cos(x)=x

(d) 11x3 - 2x2 - 77x + 14=0

3. Observe how the computed sequences converge. How many steps of the algorithm does it take to make the error less than 1e-10?

4. Compare this to the theoretical result |xi-Xi|=2-i < 10-10. Hint: solve for the number of steps i in this inequality (by hand!).

5. FSOLVE. Read about the built-in Matlab program fsolve. Use it to solve one of the above equations.

/stig