The task of synthesizing algorithm-based checking techniques for general applications is investigated. The problem is approached at the compiler level by identifying linear transformations in Fortran DO loops and restructuring program statements to convert nonlinear transformations to linear ones. System-level checks based on this property are proposed. The approach is demonstrated with example problems of matrix multiplication and the LINPACK routine: DGEFA.>
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Balasubramanian et al. (1990) studied this question.
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