The role of 𝐶*-algebras in infinite-dimensional numerical linear algebra

1994 ◽  
pp. 114-129 ◽  
Author(s):  
William Arveson
Keyword(s):  
Linear Algebra ◽  
Numerical Linear Algebra ◽  
Infinite Dimensional

scholarly journals Infinite-dimensional numerical linear algebra: theory and applications

2010 ◽  
Vol 466 (2124) ◽  
pp. 3539-3559 ◽  
Author(s):  
Anders C. Hansen
Keyword(s):  
Linear Algebra ◽  
Hilbert Spaces ◽  
Numerical Linear Algebra ◽  
New Method ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
The Core ◽  
Algebra Theory ◽  
Spectra And Pseudospectra

We present a new method for computing spectra and pseudospectra of bounded operators on separable Hilbert spaces. The core in this theory is a generalization of the pseudospectrum called the n -pseudospectrum.

scholarly journals Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices

2021 ◽  
Author(s):  
Stefano Massei
Keyword(s):  
Computer Science ◽  
Recent Work ◽  
Linear Algebra ◽  
Optimization Problems ◽  
Approximation Error ◽  
Positive Semidefinite ◽  
Numerical Linear Algebra ◽  
Maximum Volume ◽  
Deterministic Algorithms ◽  
Principal Submatrix

AbstractVarious applications in numerical linear algebra and computer science are related to selecting the $$r\times r$$ r × r submatrix of maximum volume contained in a given matrix $$A\in \mathbb R^{n\times n}$$ A ∈ R n × n . We propose a new greedy algorithm of cost $$\mathcal O(n)$$ O ( n ) , for the case A symmetric positive semidefinite (SPSD) and we discuss its extension to related optimization problems such as the maximum ratio of volumes. In the second part of the paper we prove that any SPSD matrix admits a cross approximation built on a principal submatrix whose approximation error is bounded by $$(r+1)$$ ( r + 1 ) times the error of the best rank r approximation in the nuclear norm. In the spirit of recent work by Cortinovis and Kressner we derive some deterministic algorithms, which are capable to retrieve a quasi optimal cross approximation with cost $$\mathcal O(n^3)$$ O ( n 3 ) .

scholarly journals A Note on Teaching and Learning Linear Algebra in Tribhuvan University

2019 ◽  
Vol 15 (2) ◽  
pp. 242-245
Author(s):  
Tulasi Prasad Nepal
Keyword(s):  
Linear Algebra ◽  
Teaching Methods ◽  
Teaching And Learning ◽  
Active Part ◽  
Primary Role ◽  
Group Discussions ◽  
Mathematical System ◽  
Traditional Lectures ◽  
Individual Opinion

The teaching of linear algebra has always been a challenge for teachers of mathematics, because it is extremely important that students become introduced into complex and abstract mathematical system of linear algebra and learn concepts which can be successfully applied later in other mathematical topics. It is necessary that teachers better understand how students learn, and recognize and allow that the appropriate content, methods and context could be different in different environments. As mathematicians, we are aware of the significant interconnections of different ideas and concepts, which is difficult to recognize and understand. We should not forget that understanding of these kinds of interconnections develops through active and hard exploration of mathematical topics through permanent discovering of new interconnections and relations. Thus, primary role of a teacher is to try to move students to take an active part during the class concerning important and difficult concepts, either through the form of individual opinion or through the form of group discussions. It is not easy to suggest teaching methods, especially in comparison to traditional lectures, which would be effective and would actively, engage students and generate stimulating learning.

scholarly journals Numerical Linear Algebra in Signal Processing Applications

2007 ◽  
Vol 2007 (1) ◽  
Author(s):  
Nicola Mastronardi ◽  
Gene H Golub ◽  
Shivkumar Chandrasekaran ◽  
Marc Moonen ◽  
Paul Van Dooren ◽  
...  
Keyword(s):  
Signal Processing ◽  
Linear Algebra ◽  
Numerical Linear Algebra

Special Section on Iterative Methods in Numerical Linear Algebra

1994 ◽  
Vol 15 (3) ◽  
pp. 545-546
Author(s):  
Tom Manteuffel ◽  
Steve McCormick
Keyword(s):  
Iterative Methods ◽  
Linear Algebra ◽  
Special Section ◽  
Numerical Linear Algebra
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