论文信息 - On a new class of structured matrices

On a new class of structured matrices

In this paper we continue the study of structured matrices which admit a linear complexity inversion algorithm. The new class which is studied here appears naturally as the class of matrices of input output operators for discrete time dependent descriptor linear systems. The algebra of such operators is analyzed. Multiplication and inversion algorithms of linear complexity are presented and their implementation is illustrated.

I. Gohberg | Y. Eidelman

[1] E. Asplund,et al. Inverses of Matrices $\{a_{ij}\}$ which Satisfy $a_{ij} = 0$ for $j > i+p$. , 1959 .

[2] L. Mirsky,et al. The Theory of Matrices , 1961, The Mathematical Gazette.

[3] Gene H. Golub,et al. Matrix computations , 1983 .

[4] Israel Gohberg,et al. Time varying linear systems with boundary conditions and integral operators. I. The transfer operator and its properties , 1984 .

[5] F. R. Gantmakher. The Theory of Matrices , 1984 .

[6] Israel Koltracht,et al. Linear complexity algorithm for semiseparable matrices , 1985 .

[7] Thomas Kailath,et al. A note on diagonal innovation matrices , 1987, IEEE Trans. Acoust. Speech Signal Process..

[8] Ali H. Sayed,et al. Displacement Structure: Theory and Applications , 1995, SIAM Rev..

[9] Yuli Eidelman,et al. Inversion formulas and linear complexity algorithm for diagonal plus semiseparable matrices , 1997 .

[10] Israel Gohberg,et al. Fast inversion algorithms for diagonal plus semiseparable matrices , 1997 .