The Householder - QL Matrix Diagonalisation
نویسندگان
چکیده
In this paper we report an eeective parallelisation of the House-holder routine for the reduction of a real symmetric matrix to tri-diagonal form and the QL algorithm for the diagonalisation of the resulting matrix. The Householder algorithm scales like N 3 =P + N 2 log 2 (P) and the QL algorithm like N 2 + N 3 =P as the number of processors P is increased for xed problem size. The constant parameters , , and are obtained empirically. When the eigenvalues only are required the Householder method scales as above while the QL algorithm remains sequential. The code is implemented in c in conjunction with the Message Passing Interface (MPI) libraries and veriied on a sixteen node IBM SP2 and for real matrices that occur in the simulation of properties of crystaline materials
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