Penn State Surveying Program

SUR 445
Numerical Methods in Adjustment Computations



Catalog Data 445. NUMERICAL METHODS IN ADJUSTMENT COMPUTATIONS (3) Computer optimization techniques used in adjustment of large, sparse, positive-definite matrices; efficient storage schemes. Prerequisites: SUR 242. MATH 220 and MATH 230.
Textbook Wolf, Paul R. and Ghilani, Charles D. Adjustment Computations: Statistics and Least Squares in Surveying and GIS. John Wiley & Sons, Inc.
References none
Coordinator Charles Ghilani, Professor of Engineering, Surveying Engineering Program
Goals
  1. Introduce students to storage and computation optimization techniques that are used in modern least squares programs
  2. Familiarize students with modular design of software; robust i/o procedures
  3. Familiarize students with storage and computational methods that exploit normal matrix symmetry including the Cholesky factorization process
  4. Familiarize students with band-width and column profile reordering of unknowns with emphasis on Snay's Banker's algorithm
  5. Familiarize students with numerical integration techniques and their use in computing the t, Chi2, F distribution critical values.
Prerequisites by Topic
  1. Knowledge related to the mechanics of a least squares adjustment
  2. Programming knowledge in C, Fortran, Pascal, or Basic
Topics
  1. Optimization of computer memory Usage
  2. Elements of a good program
  3. Storage strutures, the STRUCT key word
  4. Searching methods
  5. Direct formulation of the Normal matrices
  6. LU decomposition of Normal Matrix
  7. Forward and back substitution
  8. Computing an Inverse
  9. Using dynamic memory
  10. Reordering stations for storage optimization
  11. Banker's algorithm
  12. Numerical Integration using the Trapezoidal Rule,Simpson's Rule, Romberg's Method
  13. Computing the Gamma function
  14. Computing critical values for the χ2, t, and F distributions
  15. Exams
  1. 2 hours
  2. 1 hour
  3. 1 hour
  4. 3 hours
  5. 1 hour
  6. 2 hours
  7. 1 hour
  8. 2 hours
  9. 1 hour
  10. 3 hours
  11. 2 hours
  12. 3 hours
  13. 2 hours
  14. 3 hours
  15. 3 hours
Laboratories
  1. Create a program to read a horizontal data file into structures
  2. Create a program that reads a horizontal data file and generates the normal matrix directly from the observations
  3. Create a program that performs a Cholesky decomposition of a normal matrix, and solves a system of normal equations
  4. Create a program that reorders a system of observations using the banker's algorithm
  5. Develop a program to compute a critical value for a selected statistical function
  1. 2 labs
  2. 3 labs
  3. 3 labs
  4. 3 labs
  5. 4 labs
Computer Usage This course requires the students to program using C various projects. The students must also access the course notes and assignments from the Internet. Students are encouraged to submit work-using electronic mail, and have access to a chat room and electronic bulletin board for posting questions.


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Last Update: February 08, 2006