© 2016 The authors and IOS Press. The present paper describes an efficient communication optimization technique for Householder tridiagonalization called CAHTR and evaluates its parallel performance. CAHTR is intended to reduce the number of problems in collective communication, especially MPI Allreduce operations. We demonstrate the optimal version of CAHTR(3) compared with a naive implementation CAHTR(0). The CAHTR algorithms are evaluated on the K supercomputer system, and speedup exceeds x1.4 for the case of N = 5000 and P = 1024.