The LINPACK Benchmarks are a measure of a system's floating point computing power. They measure how fast a computer solves a dense N by N system of linear equations Ax = b, which is a common task in engineering. The solution is obtained by Gaussian elimination with partial pivoting, with 2/3·N3 2·N2 floating point operations. The result is reported in millions of floating point operations per second (MFLOP/s, sometimes simply called FLOPS).
Millions of floating point operations per second. A floating point operation here is a floating point addition or a floating point multiplication with 64 bit operands. For this problem there are 2/3 n^3 n^2 floating point operations.
The time in seconds to solve the problem, Ax=b.
A check is made to show that the computed solution is correct. The test is based on || Ax - b || / ( || A || || x || eps) where eps is described below. The Norm Res should be about O(1) in size. If this quantity is much larger than 1, the solution is probably incorrect.
The relative machine precision usually the smallest positive number such that fl( 1.0 - eps ) < 1.0, where fl denotes the computed value and eps is the relative machine precision.