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 -