Generalized Inverses: Theory and Computations

Wang, Guorong; Qiao, Sanzheng; Wei, Yimin

doi:10.1007/978-981-13-0146-9

Cited by 214 publications

(157 citation statements)

References 0 publications

Supporting

Mentioning

152

Contrasting

Unclassified

Order By: Relevance

“…(29) and (31), the closed-loop system is stable because all of the poles have negative real parts. Now if the velocity sensor of m 1 breaks down during the control (in other words, _ x 1 t ð Þ becomes unmeasurable), D is then changed to .…”

Section: Different Control Gainsmentioning

confidence: 99%

Partial pole assignment with time delay by the receptance method using multi-input control from measurement output feedback

Xiang

Zhen

2016

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

Section: Different Control Gainsmentioning

confidence: 99%

Partial pole assignment with time delay by the receptance method using multi-input control from measurement output feedback

Xiang

Zhen

2016

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

“…From a theoretical point of view there is interest in obtaining methods for calculating hitting times which avoid making direct use of the definition [18,36,48]. From the theory of Markov chains we know that, alternatively, the mean hitting time can be calculated via the so-called fundamental matrix associated with a finite ergodic Markov chain with stochastic matrix P , Z = (I − P + Ω) −1 where Ω = lim m→∞ P m , and for which the following equation is valid:…”

Section: Motivation and Statement Of The Problems: Hitting Times And mentioning

confidence: 99%

“…Regarding the fundamental matrix we draw attention to an important aspect of such map, namely, that Z is a particular example of a generalized inverse of the operator I − P [24,37]. As it is well-known, such inverses are in general nonunique and possess a rich algebraic theory in connection with applications to stochastic processes, linear estimation, difference equations and other areas [48]. In the setting of Markov chains, it is known that the group (Drazin) inverse enjoys a central role: if P denotes a finite stochastic matrix, A = I − P and if A # denotes its group inverse, then lim m→∞ I + P + P 2 + · · · + P m−1 m = I − AA # and several related results hold if one assumes, for instance, regularity or that the chain is absorbing.…”

Section: Motivation and Statement Of The Problems: Hitting Times And mentioning

confidence: 99%

Mean hitting times of quantum Markov chains in terms of generalized inverses

Lardizabal

2019

Quantum Inf Process

View full text Add to dashboard Cite

We study quantum Markov chains on graphs, described by completely positive maps, following the model due to S. Gudder (J. Math. Phys. 49, 072105, 2008) and which includes the dynamics given by open quantum random walks as defined by S. Attal et al. (J. Stat. Phys. 147:832-852, 2012). After reviewing such structures we examine a quantum notion of mean time of first visit to a chosen vertex. However, instead of making direct use of the definition as it is usually done, we focus on expressions for such quantity in terms of generalized inverses associated with the walk and most particularly the socalled fundamental matrix. Such objects are in close analogy with the theory of Markov chains and the methods described here allow us to calculate examples that illustrate similarities and differences between the quantum and classical settings. arXiv:1907.01313v2 [math-ph] 9 Jul 2019 Appendix: proofsThroughout the proofs we recall the notation |e I = |e I n k as n, k are clear from context.Proof of Proposition 6.3. The proof is inspired by [24]. We recall that if M ij denotes the (i, j)-th minor of a matrix A, we define the adjugate matrix as adj(A) := ((−1) i+j M ji ) 1≤i,j≤n , and it holds that A adj(A) = adj(A)A = det(A)I By Sylvester's determinant theorem, we have det(I m + AB) = det(I n + BA), from which we obtain as a consequence that det(X + |c r|) = det(X) + r| adj(X)|c

show abstract

“…In this paper, we 5 would like to follow the regulations given by Geurts. Suppose that f is a map from the data space R m 6 to the solution space R n , and R m and R n are equipped with the norms · D and · S respectively. 7 Then the absolute condition number of f at x 0 ∈ R m is defined as…”

Section: Introductionmentioning

confidence: 99%

A flexible condition number for weighted linear least squares problem and its statistical estimation

Yang

Wang

2016

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

In this paper, we mainly focus on the derivation of a flexible condition number for weighted linear least squares problem and its estimation. With Fréchet derivative and Kronecker product, the explicit expression of the condition number is obtained. When the coefficient matrices are large and dense, considering the difficulties of explicitly forming the expression of condition number in computer, we also present its simplified form through a simple and easy to operate method. Two different condition estimation methods are introduced, and the numerical experiments are also performed to show the efficiency of the condition estimators.

show abstract

Generalized Inverses: Theory and Computations

Cited by 214 publications

References 0 publications

Partial pole assignment with time delay by the receptance method using multi-input control from measurement output feedback

Partial pole assignment with time delay by the receptance method using multi-input control from measurement output feedback

Mean hitting times of quantum Markov chains in terms of generalized inverses

A flexible condition number for weighted linear least squares problem and its statistical estimation

Contact Info

Product

Resources

About