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Numerical Approximations of Diblock Copolymer Model Using a Modified Leapfrog Time-Marching Scheme
Computation, 2023 An efficient modified leapfrog time-marching scheme for the diblock copolymer model is investigated in this paper. The proposed scheme offers three main advantages.
Lizhen Chen +3 more
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More on (𝜶,𝜷)-Normal Operators in Hilbert Spaces
Abstract and Applied Analysis, 2012 We study some properties of (𝛼,𝛽)-normal operators and we present various inequalities between the operator norm and the numerical radius of (𝛼,𝛽)-normal operators on Banach algebra ℬ(ℋ) of all bounded linear operators 𝑇∶ℋ→ℋ, where ℋ is Hilbert space.
Rasoul Eskandari +2 more
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Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation
Mathematical and Computational Applications, 2019 Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of the underlying details of the chosen sparse matrix storage format. In
Conrad Sanderson, Ryan Curtin
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Numerical Linear Algebra [PDF]
, 2004 Many methods of computational statistics lead to matrix-algebra or numerical- mathematics problems. For example, the least squares method in linear regression reduces to solving a system of linear equations.
Čížek, Pavel, Čížková, Lenka
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Range Space and Similarity Transformation Using Symbolic Mathematics in Python
IEEE AccessLinear systems involved in engineering and scientific calculations can be more easily analyzed using similarity transformation. However, understanding the numerous abstract linear algebra theorems associated with this transformation can be challenging ...
Chainarong Wisassakwichai +1 more
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Gaussian elimination as an iterative algorithm [PDF]
, 2013 Gaussian elimination (GE) for solving an $n \times n$ linear system of equations $Ax=b$ is the archetypical direct method of numerical linear algebra, as opposed to iterative.
Townsend, Alex, Trefethen, Lloyd N.
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Variable-step finite difference schemes for the solution of Sturm-Liouville problems
, 2014 We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its numerical solution by means of linear algebra techniques.
Amodio, Pierluigi, Settanni, Giuseppina
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Parallel numerical linear algebra [PDF]
Acta Numerica, 1993 We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of paralled processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms.
James W. Demmel +2 more
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Aplicando o software Winplot para o ensino de sistemas de lineares.
EaD & Tecnologias Digitais na Educação, 2017 This paper describes the application of mathematical software Winplot in teaching of Linear Algebra. The use of computational resources as a didactic tool can, in addition to motivating mathematics classes, facilitate the formation of concepts and deepen
Paulo Cleber Mendonça +2 more
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Error analysis of QR algorithms for computing Lyapunov exponents [PDF]
, 2001 Lyapunov exponents give valuable information about long term dynamics. The discrete and continuous QR algorithms are widely used numerical techniques for computing approximate Lyapunov exponents, although they are not yet supported by a general error ...
Higham, D.J., McDonald, E.J.
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