Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6421243 | Applied Mathematics and Computation | 2014 | 5 Pages |
Abstract
We describe a simple implementation of the Takagi factorization of symmetric matrices A=UÎUT with unitary U and diagonal Îâ¥0 in terms of the square root of an auxiliary unitary matrix and the singular value decomposition of A. The method is based on an algebraically exact expression.For parameterized family Aε=A+εR=UεÎεUεT, εâ¥0 with distinct singular values, the unitary matrices Uε are discontinuous at the point ε=0, if the singular values of A are multiple, but the composition UεÎεUεT remains numerically stable and converges to A.The factorization is represented as a fast and compact algorithm. Its demo version for Wolfram Mathematica and interactive numerical tests are available on Internet.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Alexander M. Chebotarev, Alexander E. Teretenkov,