This paper describes the design concepts behind implementations of mixed-precision linear algebra routines targeted for the Cell processor. It describes in detail the implementation of code to solve linear system of equations using Gaussian elimination in single precision with iterative refinement of the solution to the full double-precision accuracy. By utilizing this approach the algorithm achieves close to an order of magnitude higher performance on the Cell processor than the performance offered by the standard double-precision algorithm. The code is effectively an implementation of the high-performance LINPACK benchmark, as it meets all of the requirements concerning the problem being solved and the numerical properties of the solution. Copyright © 2007 John Wiley & Sons, Ltd.