Fast verified computation for the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation

被引：4

作者：

Miyajima, Shinya ^{[1
]}

机构：

[1] Iwate Univ, Fac Sci & Engn, 4-3-5 Ueda, Morioka, Iwate 0208551, Japan

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 04期

关键词：

Nonsymmetric algebraic Riccati equation; Minimal nonnegative solution; Verified numerical computation; M-matrix; STABILIZING SOLUTIONS;

D O I：

10.1007/s40314-018-0590-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A fast iterative algorithm is proposed for numerically computing an interval matrix containing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation associated with M-matrix. This algorithm involves only cubic complexity per iteration, and moreover verifies the uniqueness of the contained solution. Numerical results show properties of the algorithm.

引用

页码：4599 / 4610

页数：12

共 19 条

[1] [Anonymous], 2008, Functions of matrices: theory and computation
[2] [Anonymous], 1962, Matrix Iterative Analysis
[3] Bini DA, 2012, FUND ALGORITHMS, V9, P1
[4] Fiedler M., 1962, Czechoslov. Math. J, V12, P382, DOI DOI 10.21136/CMJ.1962.100526
[5] Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices
Guo, CH
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2001, 23 (01) : 225 - 242
[6] Methods for verified stabilizing solutions to continuous-time algebraic Riccati equations
Haqiri, Tayyebe
Poloni, Federico
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 313 : 515 - 535
[7] Hashemi B., 2012, P SCAN C NOV, P54
[8] Horn RA, 1994, Topics in Matrix Analysis
[9] Luther W, 1999, DEV RELIABLE COMPUTI, P105
[10] Luther W, 1998, VERIFIED CALCULATION

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