CS3911 Reading List: Week 7

• Section 4.1, Section 4.2.1, Section 4.2.2 (This section was not covered in class; but, read it anyway), Section 4.3.1, Section 6.1 (read ahead), and Section 6.2 (read ahead).
• The F90 arrays and Systems of Linear Equations slides are in the common directory: F90-Array.pdf and SysLinear.pdf.

• Problems P4.7, P4.11 Do these problems without pivoting, with partial pivoting, and with complete pivoting. Then, verify your answers.

1. Count the number of multiplications used to multiply two n×n matrices.
2. Count the number of divisions in the elimination stage and the backward substitution stage of the Gaussian elimination method.
3. The following matrices A, B and C are all singular (i.e., no inverse). Note that C is the transpose of B. Use both partial and complete pivoting to eliminate the lower diagonal part of A and B. Then, use only partial pivoting to eliminate the lower diagonal part of C. What are the differences?
   

4. Find the LU-decomposition of the following matrix without pivoting, with partial pivoting, and with complete pivoting. Then, verify your results.
   

You do not have to turn in your paper. What I really expect you to do is using these problems to gauge your understanding of the subject. So, do the problems after finish reading the above sections.