Block symplectic Gram–Schmidt method

Yoichi Matsuo, Takashi Nodera


For large scale linear problems, it is common to use the symplectic Lanczos method which uses the symplectic Gram–Schmidt method to compute symplectic vectors. However, previous studies showed that the selection process of the parameter in the symplectic Gram–Schmidt method is flawed, as it results in a partially destroyed \(J\)-orthogonality of the \(J\)-orthogonal matrix. We exploree a block type symplectic Gram–Schmidt method and a new condition for the reorthogonalization to maintain \(J\)-orthogonality and to more accurately compute symplectic factorization. Applying the block size scheme to this method, we develop a new procedure for computing symplectic vectors.

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symplectic block Gram-Schmidt; optimal block size; J-orthogonality

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