| Budget Amount *help |
¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
Fiscal Year 2019: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2018: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2017: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Outline of Final Research Achievements |
A study towards the calculation of all eigenvalues of large sparse matrices was conducted. In conventional methods, large sparse matrices are treated as dense matrices, but in this study, we treated them as low-rank structured matrices. We developed a method to calculate all eigenvalues of an H-matrix (a typical low-rank structured matrix) by transforming it into a band matrix using the Householder transformation. Theoretical and numerical experiments show that the computational order can be reduced compared to the case where the matrix is treated as a dense matrix. We also developed a QR decomposition method for BLR matrices (a simple low-rank structured matrix) and its parallelization method.
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