LINPACK

The LINPACK benchmark solves a large equation system \(A \cdot x = b\) for \(x\), where \(A \in \Bbb R^{n \times n}\) and \(b,x \in \Bbb R^{n}\). The implementation does this in two separate steps: First a LU factorization is calculated for matrix \(A\). The resulting matrices \(L\) and \(U\) are used to solve the equations \(L \cdot y = b\) and finally \(U \cdot x = y\) to get the result for the vector \(x\).

Contents:

• Implementation Details
  • Kernel Design for LU Factorization
  • Performance Model for LU factorization on single FPGA
  • Multi-FPGA Implementation