TY - JOUR
T1 - An iterative method for solving the stable subspace of a matrix pencil and its application
AU - Lin, Matthew M.
AU - Chiang, Chun Yueh
N1 - Funding Information:
This research work is partially supported by the Ministry of Science and Technology of Taiwan [grant number 104-2115-M-006-017-MY3], [grant number 105-2634-E-002-001], [grant number 105-2115-M-150-001]; the National Center for Theoretical Sciences in Taiwan
PY - 2018/7/3
Y1 - 2018/7/3
N2 - This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a semigroup property depending only on the initial matrix pencil. Via this recursion relationship, we propose an accelerated iterative method to compute the stable subspace and use it to provide a theoretical result to solve the principal square root of a given matrix, both nonsingular and singular. We show that this method can not only find out the matrix square root, but also construct an iterative approach which converges to the square root with any desired order.
AB - This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a semigroup property depending only on the initial matrix pencil. Via this recursion relationship, we propose an accelerated iterative method to compute the stable subspace and use it to provide a theoretical result to solve the principal square root of a given matrix, both nonsingular and singular. We show that this method can not only find out the matrix square root, but also construct an iterative approach which converges to the square root with any desired order.
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U2 - 10.1080/03081087.2017.1348462
DO - 10.1080/03081087.2017.1348462
M3 - Article
AN - SCOPUS:85022039089
VL - 66
SP - 1279
EP - 1298
JO - Linear and Multilinear Algebra
JF - Linear and Multilinear Algebra
SN - 0308-1087
IS - 7
ER -