Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference

Dense and Banded Linear Algebraic Equation Considerations

This section provides some key points about using the dense and banded linear algebraic equation subroutines.

Use Considerations

1. To solve a system of equations, you need to use both the factorization and solve subroutines for the type of matrix you have. Each factorization subroutine should be followed in your program by the corresponding solve subroutine. The output from the factorization subroutine should be used as input to the solve subroutine.
2. To solve a system of equations with one or more right-hand sides, follow the call to the factorization subroutine with one or more calls to a solve subroutine or one call to a multiple solve |subroutine.

Performance and Accuracy Considerations

1. Except in a few instances, the _GTNP subroutines provide better performance than the _GTNPF and _GTNPS subroutines. For details, see the subroutine descriptions.
2. The general subroutines (dense and banded) use partial pivoting for accuracy and fast performance.
3. The short-precision subroutines provide increased accuracy by accumulating intermediate results in long precision. Occasionally, for performance reasons, these intermediate results are stored.
4. There are ESSL-specific rules that apply to the results of computations on the workstation processors using the ANSI/IEEE standards. For details, see What Data Type Standards Are Used by ESSL, and What Exceptions Should You Know About?.