Laboratory 2 Solving Linear Systems

Due Date: October 12

The goal of this laboratory is to implement Gaussian elimination to solve a linear system. Two programs will be required. The first involves Gaussian elimination without partial pivoting and the second builds in the partial pivoting. A comparison of both techniques is made with a badly-scaled 3 X 3 system of equations.

Instructions: Write a brief summary desribing Gaussian elimination with partial pivoting along with back substitution to find the solutions to an n X n system of equations. Write two separate programs that encode this algorithm; one with and one without partial pivoting. You may use the programming language of your choice. Your programs should be coded to handle up to a 10 X 10 system. Your programs should be well documented.

In addition, do the following.

• Run both of your programs on the following system of equations

                      -7
                1.27*10 *x_1 + 0.23*x_2  +  3.4*x_3 = 3.
  	           2.2*x_1 +  4.0*x_2  +  6.0*x_3 = -4.
  		  -2.4*x_1 +  5.0*x_2  +  7.0*x_3 = 3.3
  
  

  Compare both answers. Which is more accurate? Then use double precision (in Maple, Digits:=14) to solve this system with your Gaussian elimination program without partial pivoting. How accurate is this answer?

• Use your Gaussian elimination program with partial pivoting to solve the 5 X 5 system of equations appearing on page 323 of your text with V=5.5 volts.

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