The ScaLAPACK library contains a pair of routines for solving banded linear systems which are strictly diagonally dominant by rows. Mathematically, the algorithm is complete block cyclic reduction corresponding to a particular block partitioning of the system. In this paper we extend Heller’s analysis of incomplete cyclic reduction for block tridiagonal systems to the ScaLAPACK case. We obtain ...

Block Relative Gain (BRG) is a useful method for screening alternatives for block decentralized control at the design stage. In this paper, we establish the connection between BRG and closed loop properties like stability, input output controllability, block diagonal dominance and interactions. Based on these results, simple rules for pairing selection for block decentralized control are proposed.

It is known that the norm of the solution to a weighted linear least-squares problem is uniformly bounded for the set of diagonally dominant symmetric positive definite weight matrices. This result is extended to weight matrices that are nonnegative linear combinations of symmetric positive semidefinite matrices. Further, results are given concerning the strong connection between the boundednes...

We prove that for any λ > 1, fixed in advance, the permanent of an n × n complex matrix, where the absolute value of each diagonal entry is at least λ times bigger than the sum of the absolute values of all other entries in the same row, can be approximated within any relative error 0 < ǫ < 1 in quasi-polynomial nO(lnn−ln ǫ) time. We extend this result to multidimensional permanents of tensors ...

This paper describes an efficient and robust hybrid parallel solver ‘‘the SPIKE algorithm’’ for narrow-banded linear systems. Two versions of SPIKE with their built-in-options are described in detail: the Recursive SPIKE version for handling non-diagonally dominant systems and the Truncated SPIKE version for diagonally dominant ones. These SPIKE schemes can be used either as direct solvers, or ...

We report on experiments with a stable algorithm for the parallel solution of banded and periodically banded linear systems. In contrast to most of the known parallel algorithms which are stable only for symmetric positive deenite or diagonally dominant systems, the new algorithm incorporates pivoting without sacriicing eeciency. We report on numerical experiments conducted on an Intel Paragon,...

In this paper a new method for robust decentralised control of large-scale systems using quantitative feedback theory (QFT ) is suggested. For a given largescale system an equivalent descriptor system is defined. Using this representation, closed-loop diagonal dominance sufficient conditions over the uncertainty space are derived. It is shown by appropriately choosing output disturbance rejecti...

Guangbin Wang, Hao Wen, and Ting Wang Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China Correspondence should be addressed to Guangbin Wang, [email protected] Received 11 June 2011; Revised 20 September 2011; Accepted 22 September 2011 Academic Editor: Yongkun Li Copyright q 2011 Guangbin Wang et al. This is an open access article distributed ...

We report on numerical experiments that we conducted with a direct algorithm, the single width sparator algorithm, to solve diagonally dominant banded linear systems. With detailed estimations of computation and communication cost we quantitatively analyze their innuence on the parallel performance of the algorithm. We report on numerical experiments executed on an Intel Paragon XP/S-22MP.

We present several results that rely on arguments involving the combinatorics of “bushy trees”. These include the fact that there are arbitrarily slow-growing diagonally noncomputable (DNC) functions that compute no Kurtz random real, as well as an extension of a result of Kumabe in which we establish that there are DNC functions relative to arbitrary oracles that are of minimal Turing degree. ...