程序代写代做代考 algorithm checklist.dvi
checklist.dvi
ECS130 Mini-Project Grading Check List
1. Summary (abstract)
What is the mathematical problem of this report about? What is your solution? What is
your finding?
2. Introduction of the main problem
Statement of the problem: the linear least squares problem minβ ‖Xβ − b‖
(Background) When X is nonsingular, …. normal equation and QR decomposition
(Purpose of this project) We study the solution of the LS when when X is singular.
3. Definitions (tools/theory) needed:
rank deficient, singular value decomposition, pseudo-inverse
4. Algorithms
(a) β = Xy (why not use)
(b) β = pinv(X, tol)y with different drop tolerance values tol pinv(X) uses the default
tolerance value.
(c) β = V Σ+UT y, where X = UΣV T is the SVD of X, Σ+ is defined with with a drop
tolerance value tol
Note that Algorithms (b) and (c) are essentially the same.
5. Numerical examples
Use the Problem 5.6 and shaw.m to illustrate the key finding:
The accuracy (measured in the relative error) of the computed solution strongly
depends on the drop tolerance value “tol” in pinv (or say SVD).
Here are numerical results in plots for the Shaw problem to support the key finding:
0 10 20 30 40 50 60 70 80 90 100
0
0.5
1
1.5
2
2.5
exact and computed solution
exact
computed with default tol
0 10 20 30 40 50 60 70 80 90 100
−0.5
0
0.5
1
1.5
2
2.5
exact and computed solution
exact
computed with tol = 1e−15
0 10 20 30 40 50 60 70 80 90 100
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
10
1
Relative errors
rel err with default tol
rel error with tau=1e−15
6. Conclusion
Recap of the problem, the solution method and key finding.
7. Acknowledgement if any
8. References
1
