Anymatrix: an extensible MATLAB matrix collection

Higham, Nicholas J.; Mikaitis, Mantas

doi:10.1007/s11075-021-01226-2

Cited by 11 publications

(10 citation statements)

References 42 publications

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“…A particular convenient way of approximating it by numerical quadrature arises from its Stieltjes representation 1. We selected all matrices with properties square and non-singular from the anymatrix collection [19]. 2.…”

Section: Discussionmentioning

confidence: 99%

“…While our exact expression in fact agrees with the lower bound that was previously available, it is instructive to compare it to the upper bounds (11): Whenever it is of interest to use the condition number in order to obtain accuracy guarantees for a computed result, upper bounds are of much more use than lower bounds. In this experiment, we compare ( 11) and ( 20) for matrices from the anymatrix collection [19] 1 . Specifically, we select all matrices which .…”

Section: The Level-2 Condition Number Of Some Classes Of Functions Of...mentioning

confidence: 99%

“…⋄ Experiment 17. In our last experiment, we test the accuracy of our method on a wide variety of matrices from the anymatrix collection [19], most of which are non-Hermitian and non-normal. See Appendix B for details on the data set that is used.…”

Section: Numerical Experimentsmentioning

confidence: 99%

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Integral representations for higher-order Fréchet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number

Schweitzer¹

2022

Preprint

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We propose an integral representation for the higher-order Fréchet derivative of analytic matrix functions f (A) which unifies known results for the first-order Fréchet derivative of general analytic matrix functions and for higher-order Fréchet derivatives of A −1 . We highlight two applications of this integral representation: On the one hand, it allows to find the exact value of the level-2 condition number (i.e., the condition number of the condition number) of f (A) for a large class of functions f when A is Hermitian. On the other hand, it also allows to use numerical quadrature methods to approximate higher-order Fréchet derivatives. We demonstrate that in certain situations-in particular when the derivative order k is moderate and the direction terms in the derivative have low-rank structure-the resulting algorithm can outperform established methods from the literature by a large margin.

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Section: Discussionmentioning

confidence: 99%

Section: The Level-2 Condition Number Of Some Classes Of Functions Of...mentioning

confidence: 99%

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Integral representations for higher-order Fréchet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number

Schweitzer¹

2022

Preprint

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“…Remark 5: The matrix D denotes the communication matrix for the Kronecker product, which has the same property provided in [46, Lemma 2]. In addition, it can be obtained by solving MATLAB function vecperm(q, ν) [47].…”

Section: E Closed-loop System Of Wpsmentioning

confidence: 99%

Sampled Memory-Event-Triggered Fuzzy Load Frequency Control for Wind Power Systems Subject to Outliers and Transmission Delays

Yan

Park

et al. 2023

IEEE Trans. Cybern.

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This study is devoted to event-triggered fuzzy load frequency control (LFC) for wind power systems (WPSs) with measurement outliers and transmission delays. Due to the integration of wind turbine (WT) with nonlinearity, the T-S fuzzy model of WPS is established for stability analysis and controller design. To mitigate the network burden, a new sampled memoryevent-triggered mechanism (SMETM) related to historical system information is presented. It has the following two merits: 1) the utilization of continuous memory outputs over a given interval is useful to reduce the information loss in the period of samples and the redundant triggering events induced by disturbances and noises and 2) an extra upper constraint is added in the triggering condition to generate a new event only when the error signal belongs to a bounded range, thus, the false events caused by measurement outliers can be differentiated out and then be dropped. By representing the memory signal with transmission delay as a time-varying distributed delay term, a T-S fuzzy time-varying distributed delay system is built up to model the H ∞ LFC WPS. With the help of the Lyapunov method and the integral inequality relying on distributed delay, some criteria are derived to solve the triggering matrix and fuzzy controllers. Finally, the merits of the proposed SMETM are tested by simulation results.

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“…If S is the Schur complement of A 11 in A, defined in (6), and S = UU T is the Reverse Cholesky decomposition of S, then L 22 = L −T 11 = U .…”

Section: Lemma 4 Every Symmetric Positive Definite Symplectic Matrix ...mentioning

confidence: 99%

On computing the symplectic LLT factorization

2022

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We analyze two algorithms for computing the symplectic factorization A = LLT of a given symmetric positive definite symplectic matrix A. The first algorithm W1 is an implementation of the HHT factorization from Dopico and Johnson (SIAM J. Matrix Anal. Appl. 31(2):650–673, 2009), see Theorem 5.2. The second one is a new algorithm W2 that uses both Cholesky and Reverse Cholesky decompositions of symmetric positive definite matrices. We present a comparison of these algorithms and illustrate their properties by numerical experiments in MATLAB. A particular emphasis is given on symplecticity properties of the computed matrices in floating-point arithmetic.

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Anymatrix: an extensible MATLAB matrix collection

Cited by 11 publications

References 42 publications

Integral representations for higher-order Fréchet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number

Integral representations for higher-order Fréchet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number

Sampled Memory-Event-Triggered Fuzzy Load Frequency Control for Wind Power Systems Subject to Outliers and Transmission Delays

On computing the symplectic LLT factorization

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