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1. Exercises 2.10, 2.16, 2.19 in the page 78~79 of the Textbook.
2. Why are almost all high performance computing implemented on Linux OS?
Please look for the relevant information on the Internet, and give the 3 to 5
most important reasons that you think of.
3. In numerical linear algebra, the Jacobi method (or Jacobi iterative
method) is an algorithm for determining the solutions of a diagonally
dominant system of linear equations. Each diagonal element is solved for,
and an approximate value is plugged in. The process is then iterated until
it converges. This algorithm is a stripped-down version of the Jacobi
transformation method of matrix diagonalization.
Let
?? = ?
be a square system of n linear equations, where:
Then A can be decomposed into a diagonal component D, and the
remainder R:
The solution is then obtained iteratively via
?(?+1) = ??1(? ? ??(?)
)
where ?(?) is the kth approximation or iteration of x and ?(?+1) is the
next or (? + 1)?? iteration of x. The element-based formula is thus:
A sufficient (but not necessary) condition for the method to converge is
that the matrix A is strictly or irreducibly diagonally dominant. Strict row
diagonal dominance means that for each row, the absolute value of the
diagonal term is greater than the sum of absolute values of other terms:
Please write a sequential C program to implement solving a system of
Linear Equations by Jacobi iterative method, and suppose the method is
simply convergent.
Note: When you try to implement your sequential programs, please just call
some basic (standard) C library functions or routines, in case of being the
inconvenience when you are going to implement the corresponding parallel
versions in future.