Related papers: Singular Value Decomposition at FIFA 2022
Square matrices of the form $\widetilde{\mathbf{A}} =\mathbf{A} + \mathbf{e}D \mathbf{f}^*$ are considered. An explicit expression for the inverse is given, provided $\widetilde{\mathbf{A}}$ and $D$ are invertible with…
Classification of matches played in the last rounds of sports competitions is a well-established tool for evaluating tournament designs. Both deterministic and probabilistic approaches are available for this purpose. Our paper offers the…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
The local zero structure of a smooth map may qualitatively change, when the map is subjected to small perturbations. The changes may include births and/or deaths of zeros. The qualitative properties are defined as the invariances of an…
In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input…
Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…
Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern…
A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets…
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the…
This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar…
Convergence of a matrix decomposition technique, the multi-field singular value decomposition (MFSVD) which efficiently analyzes nonlinear correlations by simultaneously decomposing multiple fields, is investigated. Toward applications in…
This is a note on my mini-course in the International Workshop on Real and Complex Singularities held at ICMC-USP (Sao Carlos, Brazil) in July 2012. Here we introduce a new branch of the Thom polynomial theory for singularities of…
This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the…
In this paper two ways to compute singular values are presented which use Cholesky decomposition as their basic operation.
If the final position of a team is already secured independently of the outcomes of the remaining games in a round-robin tournament, it might play with little enthusiasm. This is detrimental to attendance and can inspire collusion and…
The group stage of a sports tournament is often made more appealing by introducing additional constraints in the group draw that promote an attractive and balanced group composition. For example, the number of intra-regional group matches…
This paper explores a novel way for analyzing the tournament structures to find a best suitable one for the tournament under consideration. It concerns about three aspects such as tournament conducting cost, competitiveness development and…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…
The cylindrical algebraic decomposition (CAD) is the only complete method used in practice for solving problems like quantifier elimination or SMT solving related to real algebra, despite its doubly exponential complexity. Recent…