# An iterative method for solving the stable subspace of a matrix pencil and its application

Matthew M. Lin, Chun Yueh Chiang

Research output: Contribution to journalArticle

### Abstract

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.

Original language English 1279-1298 20 Linear and Multilinear Algebra 66 7 https://doi.org/10.1080/03081087.2017.1348462 Published - 2018 Jul 3

### Fingerprint

Matrix Pencil
Subspace
Iteration
Square root
Matrix Square Root
Singular matrix
Nonsingular or invertible matrix
Null Space
Recursion
Semigroup
Converge

### All Science Journal Classification (ASJC) codes

• Algebra and Number Theory

### Cite this

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In: Linear and Multilinear Algebra, Vol. 66, No. 7, 03.07.2018, p. 1279-1298.

Research output: Contribution to journalArticle

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AU - Chiang, Chun Yueh

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