Fast enclosure for a matrix inverse square root. (English) Zbl 1305.65133
Summary: A fast algorithm for computing an interval matrix containing the inverse square root of an \(n \times n\) matrix \(A\) is proposed. This algorithm utilizes numerical spectral decomposition of \(A\) and requires only \(\mathcal{O}(n^3)\) operations. The principal property and uniqueness of the contained inverse square root can moreover be verified by the proposed algorithm. Numerical results show the effectiveness and efficiency of this algorithm.
MSC:
| 65F30 | Other matrix algorithms (MSC2010) |
| 65G30 | Interval and finite arithmetic |
| 65F05 | Direct numerical methods for linear systems and matrix inversion |
| 65G20 | Algorithms with automatic result verification |
Keywords:
matrix function; matrix inverse square root; numerical enclosure; verified computation; interval matrix; algorithm; spectral decomposition; numerical resultReferences:
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