@techreport{oai:ipsj.ixsq.nii.ac.jp:00158496,
 author = {Shohei, Kobayashi and Shohei, Kobayashi},
 issue = {6},
 month = {Apr},
 note = {Linear systems are solved by LU decomposition. Partial pivoting is the most frequently employed way to perform this decomposition. Pivoting is necessary for numerical stability of LU decomposition. However, pivoting is not able to be computed in parallel and pivoting restricts block LU decomposition algorithms. A no-pivoting LU decomposition algorithm has been investigated for more than two decades. This decomposition algorithm without pivoting is efficient for modern computers. However, stabilizing numerical accuracy of solutions of linear systems without pivoting is more difficult than partial pivoting. This thesis researches the algorithm called RDFT that eliminates pivoting nessesity by using random numbers and discrete Fourier transform. We show some examples of LU decomposition by RDFT fail numerically. In addition, we improve the RDFT algorithm with modification to improve numerical stability of such matrices., Linear systems are solved by LU decomposition. Partial pivoting is the most frequently employed way to perform this decomposition. Pivoting is necessary for numerical stability of LU decomposition. However, pivoting is not able to be computed in parallel and pivoting restricts block LU decomposition algorithms. A no-pivoting LU decomposition algorithm has been investigated for more than two decades. This decomposition algorithm without pivoting is efficient for modern computers. However, stabilizing numerical accuracy of solutions of linear systems without pivoting is more difficult than partial pivoting. This thesis researches the algorithm called RDFT that eliminates pivoting nessesity by using random numbers and discrete Fourier transform. We show some examples of LU decomposition by RDFT fail numerically. In addition, we improve the RDFT algorithm with modification to improve numerical stability of such matrices.},
 title = {Numerical Unstability and Improvement of a No-Pivoting LU Decomposition Algorithm by a Discrete Fourier Matrix},
 year = {2016}
}