@article{oai:nagoya.repo.nii.ac.jp:00009072, author = {山本, 有作 and Yamamoto, Yusaku}, issue = {2}, journal = {日本応用数理学会論文誌}, month = {Jun}, note = {The Algorithm of Multiple Relatively Robust Representations (MR^3) is a new algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem proposed by I.Dhillon in 1997. It has attracted much attention because it can compute all the eigenvectors of an n x n matrix in only O(n^2) work and is easy to parallelize. In this article, we survey the papers related to the MR^3 algorithm and try to present a simple and easily understandable picture of the algorithm by explaining, one by one, its key ingredients such as the relatively robust representations of a symmetric tridiagonal matrix, the dqds algorithm for computing accurate eigenvalues and the twisted factorization for computing accurate eigenvectors. Limitations of the algorithm and directions for future research are also discussed.}, pages = {181--208}, title = {密行列固有値解法の最近の発展(I) : Multiple Relatively Robust Representationsアルゴリズム}, volume = {15}, year = {2005} }