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A new inverse iteration algorithm that can be used to compute all theeigenvectors of a real symmetric tri-diagonal matrix on parallel computers isdeveloped. The modified Gram-Schmidt orthogonalization is used in the classicalinverse iteration. This algorithm is sequential and causes a bottleneck inparallel computing. In this paper, the use of the compact WY representation isproposed in the orthogonalization process of the inverse iteration with theHouseholder transformation. This change results in drastically reducedsynchronization cost in parallel computing. The new algorithm is evaluated onboth an 8-core and a 32-core parallel computer, and it is shown that the newalgorithm is greatly faster than the classical inverse iteration algorithm incomputing all the eigenvectors of matrices with several thousand dimensions.

On Implementation and Evaluation of Inverse Iteration Algorithm with compact WY Orthogonalization