Asymptotic Analysis of a New Multishift QR Method for Symmetric Tridiagonal Eigenproblems(Theory,Aigorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2008)

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  • 対称三重対角行列向けマルチシフトQR法の漸近的収束性解析(理論,行列・固有値問題の解法とその応用,<特集>平成20年研究部会連合発表)
  • 対称三重対角行列向けマルチシフトQR法の漸近的収束性解析
  • タイショウ 3ジュウ タイカク ギョウレツ ムケ マルチシフト QRホウ ノ ゼンキンテキ シュウソクセイ カイセキ

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The Multishift QR method (M-QR) enables us to compute all the eigenvalues of a symmetric tridiagonal matrix on parallel machines. To use all processors sufficiently, the Deferred shift QR method (D-QR) is proposed. However, the convergence rate of D-QR is numerically inferior to that of M-QR. Recently, the Fully Pipelined Multishift QR method (FPM-QR) is proposed. FPM-QR shows better convergence than D-QR while keeping the high level of processor utilization. In this paper, we analyze the asymptotic behavior of FPM-QR with two shifts.

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