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HOSVD-based Canonical Form Of TP Functions And QLPV Models
Baranyi and Yam proposed the concept of M-mode SVD/HOSVD-based canonical form of TP functions and quasi-LPV system models. Szeidl et al. proved that the TP model transformation is capable of numerically reconstructing this canonical form. Baranyi and Yam employed the ideas described by De Lathauwer ''etal'' and the algorithm developed by Vasilescu and Terzopoulos under the name M-mode SVD. The M-mode SVD is referred in the literature as either the Tucker or the HOSVD. The Tucker algorithm and the DeLathauwer ''etal.'' companion algorithm are sequential algorithm that employ gradient descent or the power method, respectively. Related definitions (on TP functions, finite element TP functions, and TP models) can be found here. Details on the control theoretical background (i.e., the TP type polytopic Linear Parameter-Varying state-space model) can be found here. A free MATLAB implementation of the TP model transformation can be downloaded aor at MATLAB Centra Existence of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HOSVD
In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one type of generalization of the matrix singular value decomposition. It has applications in computer vision, computer graphics, machine learning, scientific computing, and signal processing. Some aspects can be traced as far back as F. L. Hitchcock in 1928, but it was L. R. Tucker who developed for third-order tensors the general Tucker decomposition in the 1960s, further advocated by L. De Lathauwer ''et al.'' , or advocated by Vasilescu and Terzopoulos. Although the term HOSVD was coined by De Lathauwer, the algorithm most commonly referred to as the Tucker or Higher-Order Singular Value Decomposition (HOSVD) in the literature was originally introduced by Vasilescu and Terzopoulos under the name M-mode SVD.M. A. O. Vasilescu, D. Terzopoulos (2002), "Multilinear Analysis of Image Ensembles: TensorFaces," Proc. 7th Euro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Form
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way. The distinction between "canonical" and "normal" forms varies from subfield to subfield. In most fields, a canonical form specifies a ''unique'' representation for every object, while a normal form simply specifies its form, without the requirement of uniqueness. The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero. More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific object in each class. For example: *Jordan normal form is a canonical form for matrix similarity. *The row echelon form is a canonical form, when one considers as equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TP Model Transformation
In mathematics, the tensor product (TP) model transformation was proposed by Baranyi and Yam as key concept for higher-order singular value decomposition of functions. It transforms a function (which can be given via closed formulas or neural networks, fuzzy logic, etc.) into TP function form if such a transformation is possible. If an exact transformation is not possible, then the method determines a TP function that is an approximation of the given function. Hence, the TP model transformation can provide a trade-off between approximation accuracy and complexity. A free MATLAB implementation of the TP model transformation can be downloaded a or an old version of the toolbox is available at MATLAB Centra A key underpinning of the transformation is the higher-order singular value decomposition. Besides being a transformation of functions, the TP model transformation is also a new concept in qLPV based control which plays a central role in the providing a valuable means of bridgin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TP Model Transformation In Control Theories
TP may refer to: Arts and entertainment Music * Test pressing, of a vinyl record * Tonic parallel (Tp and tP), in music theory * ''TP'' (Teddy Pendergrass album), 1980 * ''TP'' (Tony Parker album), 2007 * Tonus Peregrinus (vocal ensemble), a British group * Either of two R&B albums by R. Kelly: ** '' TP-2.com'', 2000 ** '' TP.3 Reloaded'', 2005 Other media * '' The Legend of Zelda: Twilight Princess'', a Nintendo video game * Test pattern or test card, a broadcast television signal * '' Tahanang Pinakamasaya'', a Filipino variety show * '' The Times-Picayune , The New Orleans Advocate'', an American daily newspaper * ''The Tomorrow People'', a British science fiction television series Businesses and organizations Technology brands and businesses * TP-Link, a global manufacturer of computer networking products * TP Vision, a subsidiary of TPV Technology, Amsterdam, Netherlands * Telekomunikacja Polska (now ''Orange Polska''), a Polish telecommunications provider * Thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kronecker Delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: \delta_ = \begin 0 &\text i \neq j, \\ 1 &\text i=j. \end or with use of Iverson brackets: \delta_ = =j, For example, \delta_ = 0 because 1 \ne 2, whereas \delta_ = 1 because 3 = 3. The Kronecker delta appears naturally in many areas of mathematics, physics, engineering and computer science, as a means of compactly expressing its definition above. Generalized versions of the Kronecker delta have found applications in differential geometry and modern tensor calculus, particularly in formulations of gauge theory and topological field models. In linear algebra, the n\times n identity matrix \mathbf has entries equal to the Kronecker delta: I_ = \delta_ where i and j take the values 1,2,\cdots,n, and the inner product of vectors can be written as \mathbf\cdot\mathbf = \sum_^n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
