A DIRECT SOLUTION TO THE BLOCK TRIDIAGONAL MATRIX INVERSION PROBLEM

Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.

Download Full-text

Spectral Algorithms for Supervised Learning

Neural Computation ◽

10.1162/neco.2008.05-07-517 ◽

2008 ◽

Vol 20 (7) ◽

pp. 1873-1897 ◽

Cited By ~ 44

Author(s):

L. Lo Gerfo ◽

L. Rosasco ◽

F. Odone ◽

E. De Vito ◽

A. Verri

Keyword(s):

Kernel Methods ◽

Classification Performance ◽

Matrix Inversion ◽

Regularization Methods ◽

Data Sets ◽

Inversion Problem ◽

Spectral Regularization ◽

Numerical Stabilization ◽

Ill Posed ◽

Real World Problems

We discuss how a large class of regularization methods, collectively known as spectral regularization and originally designed for solving ill-posed inverse problems, gives rise to regularized learning algorithms. All of these algorithms are consistent kernel methods that can be easily implemented. The intuition behind their derivation is that the same principle allowing for the numerical stabilization of a matrix inversion problem is crucial to avoid overfitting. The various methods have a common derivation but different computational and theoretical properties. We describe examples of such algorithms, analyze their classification performance on several data sets and discuss their applicability to real-world problems.

Download Full-text

A Covariance Matrix Inversion Problem arising from the Construction of Phylogenetic Trees

LMS Journal of Computation and Mathematics ◽

10.1112/s1461157000001327 ◽

2007 ◽

Vol 10 ◽

pp. 119-131

Author(s):

Tom M. W. Nye ◽

Brad J. C. Baxter ◽

Walter R. Gilks

Keyword(s):

Phylogenetic Tree ◽

Phylogenetic Trees ◽

Symmetric Matrix ◽

Matrix Inversion ◽

Covariance Matrices ◽

Inner Product ◽

Inversion Problem ◽

Inversion Algorithm ◽

Tree Construction ◽

Under Construction

AbstractWe describe an efficient algorithm for the inversion of covariance matrices that arise in the context of phylogenetic tree construction. Phylogenetic trees describe the evolutionary relationships between species, and their construction is computationally demanding. Many approaches involve the symmetric matrix of evolutionary distances between species. Regarding these distances as random variables, the corresponding set of variances and covariances form a rank-4 tensor, and the inner-product defined by its inverse can be used to assign statistical scores to candidate trees. We describe a natural set of assumptions for the phylogenetic tree under construction, and show how under these assumptions the covariance tensor for a tree with n leaves can be inverted in O(n2) operations. In addition to presenting the inversion algorithm, we hope this article will open algebraic and computational problems from the field of phylogeny to a wider audience.

Download Full-text

Anatomy and ultrastructure of haustoria in selected West Australian parasitic angiosperms

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010016100x ◽

1990 ◽

Vol 48 (3) ◽

pp. 690-691

Author(s):

John Kuo ◽

John S. Pate

Keyword(s):

Parasitic Plants ◽

The Other ◽

Nutrient Transfer ◽

Direct Solution ◽

Tracheary Elements ◽

Solute Transfer ◽

Glycol Methacrylate ◽

Australian Species ◽

Anatomy And Ultrastructure ◽

Solution Transfer

Our understanding of nutrient transfer between host and flowering parasitic plants is usually based mainly on physiological concepts, with little information on haustorial structure related to function. The aim of this paper is to study the haustorial interface and possible pathways of water and solute transfer between a number of host and parasites.Haustorial tissues were fixed in glutaraldehyde and embedded in glycol methacrylate (LM), or fixed in glutaraldehyde then OsO4 and embedded in Spurr’s resin (TEM).Our study shows that lumen to lumen continuity occurs between tracheary elements of a host and four S.W. Australian species of aerial mistletoes (Fig. 1), and some root hemiparasites (Exocarpos spp. and Anthobolus foveolatus) (Fig. 2). On the other hand, haustorial interfaces of the root hemiparasites Olax phyllanthi and Santalum (2 species) are comprised mainly of parenchyma, as opposed to terminating tracheads or vessels, implying that direct solution transfer between partners via vessels or tracheary elements may be limited (Fig. 3).

Download Full-text

The LQG game with nonclassical information pattern using a direct solution method

2017 American Control Conference (ACC) ◽

10.23919/acc.2017.7962989 ◽

2017 ◽

Author(s):

Joshua W. Clemens ◽

Jason L. Speyer

Keyword(s):

Solution Method ◽

Direct Solution ◽

Direct Solution Method ◽

Information Pattern ◽

Nonclassical Information

Download Full-text

The Tax Inversion Problem: A Hard Nut to Crack

SSRN Electronic Journal ◽

10.2139/ssrn.2978207 ◽

2017 ◽

Author(s):

Phillip Fuller ◽

Henry Thomas

Keyword(s):

Inversion Problem

Download Full-text

Tailoring the physical characteristics of solution blown cellulosic nonwovens by various post-treatments

Nordic Pulp & Paper Research Journal ◽

10.1515/npprj-2021-0025 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Kerstin Jedvert ◽

Linnea Viklund ◽

Mårten Alkhagen ◽

Tobias Köhnke ◽

Hans Theliander

Keyword(s):

Ionic Liquid ◽

Physical Characteristics ◽

Direct Solution ◽

Post Processing ◽

Drying Method ◽

Solution Blowing ◽

Renewable Feedstock ◽

Processing Steps

Abstract Nonwovens are increasing in demand due to their versatility which enables use in a broad range of applications. Most nonwovens are still produced from fossil-based resources and there is thus a need to develop competitive materials from renewable feedstock. In this work, nonwovens are produced from cellulose via a direct solution blowing method. Cellulose was dissolved using the ionic liquid 1-ethyl-3-methylimidazolium acetate (EMIMAc) and was regenerated into nonwovens by coagulation in water. The properties of such nonwovens were previously rather stiff and papery-like and the aim of this work was to improve the softness and feel of the materials by simple adjustments of the post-processing steps, i. e. washing and drying. It was shown that by primarily changing the drying method, it was possible to create a much softer and bulkier material using the same solution blowing parameters.

Download Full-text