Linpack 1.5.1

Linpack Benchmark

The LINPACK Benchmarks are a measurement of a system's floating-point computing power. They assess how efficiently a computer can solve a dense N by N system of linear equations Ax = b, a common engineering task. This solution is achieved through Gaussian elimination with partial pivoting, involving 2/3·N3 + 2·N2 floating-point operations. The outcome is detailed in millions of floating-point operations per second (MFLOP/s, sometimes referred to as FLOPS).

Results:

• Mflop/s: Millions of floating-point operations per second. A floating-point operation in this context refers to a float-point addition or multiplication with 64-bit operands. For this particular problem, it involves 2/3 n^3 + n^2 floating-point operations.
• Time: The duration in seconds required to solve the Ax=b problem.
• Norm Res: This evaluates the correctness of the computed solution by checking || Ax - b || / ( || A || || x || eps), where eps is elaborated below. The Norm Res should typically be around O(1) in magnitude. A significantly larger quantity may indicate an inaccurate solution.
• Precision: It determines the relative machine precision, typically the smallest positive number ensuring fl(1.0 - eps) < 1.0, where fl denotes the calculated value and eps denotes the relative machine precision.