General Considerations


Unless the A matrix is very sparse, you will not be able to solve the initial system of equations directly. Methods to solve a system of equations for the vector of unknowns involve changing the A matrix into a form such that the unknowns can be solved for directly. The process of converting the A matrix makes use of three linear algebra relations ”

  1. You can add a multiple of any row of the A matrix to any other row without altering the solution. Whatever is done to the A matrix must also be done to the b vector. If you add two times the third row of the A matrix to the fourth row of the A matrix, you must also add two times the third b element to the fourth b element.

  2. You can interchange two rows of the A matrix and b vector without changing the solution. This is equivalent to writing the system of equations in a different order.

  3. You can switch two columns of the A matrix if you also switch the corresponding rows of the b vector.

All of the methods discussed in this chapter overwrite the original A matrix during the solution process. If you want to retain the original A matrix, you will have to make a copy of it before solving the system of equations.



Technical Java. Applications for Science and Engineering
Technical Java: Applications for Science and Engineering
ISBN: 0131018159
EAN: 2147483647
Year: 2003
Pages: 281
Authors: Grant Palmer

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