Orthogonal decomposition of derivatives and antiderivatives for easy evaluation of extended Gram matrix

Telescu, Mihai; Brehonnet, P.; Tanguy, Noël; Vilbe, P.; Calvez, L.C.

doi:10.1016/j.sigpro.2006.06.007

Cited by 2 publications

(3 citation statements)

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“…The amount of computation mainly focuses on matrix multiplication [29] and contains two parts: one is the computation of initial basic interval, and another is times merging during the addition theorem. The amount of computation is about [( + − 1) 3 + ( + − 1) 2 ], in which is the weighting coefficient of matrix A (see (15)), q represents the order of Taylor expansion series (see (16), (17)), m is number of columns of matrix B, and is order of matrix A.…”

Section: Programming Flow Chart Of the Methodmentioning

confidence: 99%

“…But in practice, most of the system matrices are not in conformity with the forms above; the order is large or even system matrix is singular in some cases; analytical method is essentially useless; some other methods can be used to solve it. A variety of methods permit a both fast and accurate computation of the Gram matrix of system [11][12][13][14][15][16]. In [11], a method for evaluation of the Gram matrix from the coefficients of the system transfer function is proposed, but it is tedious and cumbersome; the methods proposed in [12][13][14] computed Gram matrix using its properties in time-domain, but as the authors stated, the technique though very elegant in principle it gives poor results due to two reasons.…”

Section: Introductionmentioning

confidence: 99%

“…But it is relatively applied in a narrow scope and not suited for irrational resonant system. In [16], a method for evaluation of the Gram matrix via a Kautz model is proposed. However, the efficiency or accuracy of the computation heavily depends on the choice of Kautz parameters, and it is also only suitable for stable systems.…”

Section: Introductionmentioning

confidence: 99%

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Computation of Gram Matrix and Its Partial Derivative Using Precise Integration Method for Linear Time-Invariant Systems

Ren

Bao

et al. 2014

Journal of Applied Mathematics

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Gram matrix is an important tool in system analysis and design as it provides a description of the input-output behavior for system; its partial derivative matrix is often required in some numerical algorithms. It is essential to study computation of these matrices. Analytical methods only work in some special circumstances; for example, the system matrix is diagonal matrix or Jordan matrix. In most cases, numerical integration method is needed, but there are two problems when compute using traditional numerical integration method. One is low accuracy: as high accuracy requires extremely small integration step, it will result in large amount of computation; and another is stability and stiffness issues caused by the dependence on the property of system matrix. In order to overcome these problems, this paper proposes an efficient numerical method based on the key idea of precise integration method (PIM) for the Gram matrix and its partial derivative of linear time-invariant systems. Since matrix inverse operation is not required in this method, it can be used with high precision no matter the system is normal or singular. The specific calculation algorithm and block diagram are also given. Finally, numerical examples are given to demonstrate the correctness and validity of this method.

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Section: Programming Flow Chart Of the Methodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computation of Gram Matrix and Its Partial Derivative Using Precise Integration Method for Linear Time-Invariant Systems

Ren

Bao

et al. 2014

Journal of Applied Mathematics

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Efficient Gram-matrix computation for irrational resonant systems using Kautz models

Telescu¹,

Tanguy²,

Brehonnet³

et al. 2007

Signal Processing

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To cite this version:Mihai Telescu, Noël Tanguy, Pascale Bréhonnet, Pierre Vilbé. Efficient Gram-matrix computation for irrational resonant systems using Kautz models. Signal Processing, Elsevier, 2007, 87 (12) AbstractWe present a new method for evaluating the Gram matrix containing the inner products of repeated integrals and derivatives of irrational transfer functions via a Kautz model. The technique is particularly interesting for describing resonant systems and it has an immediate application in model order reduction.

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Orthogonal decomposition of derivatives and antiderivatives for easy evaluation of extended Gram matrix

Cited by 2 publications

References 14 publications

Computation of Gram Matrix and Its Partial Derivative Using Precise Integration Method for Linear Time-Invariant Systems

Computation of Gram Matrix and Its Partial Derivative Using Precise Integration Method for Linear Time-Invariant Systems

Efficient Gram-matrix computation for irrational resonant systems using Kautz models

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