Article ID Journal Published Year Pages File Type
6421243 Applied Mathematics and Computation 2014 5 Pages PDF
Abstract

We describe a simple implementation of the Takagi factorization of symmetric matrices A=UΛUT with unitary U and diagonal Λ≥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=UεΛεUεT, ε≥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 UεΛεUεT 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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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