On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems
TLDR
In this article, it was shown that the generalized conjugate-gradient (CC) can be simplified if a nonsingular matrix H is available such that HA = ATH.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-07-01 and is currently open access. It has received 73 citations till now. The article focuses on the topics: Conjugate gradient method & Identity matrix.read more
Citations
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Book ChapterDOI
High-Performance Computing for Real-Time Grid Analysis and Operation
TL;DR: In this article, power system computation software tools are traditionally designed as serial codes and optimized for single-processor computers They are becoming inadequate in terms of computational efficiency for the ever increasing complexity of the power grid The power grid has served us remarkably well but is likely to see more changes over the next decade than it has seen over the past century.
Journal ArticleDOI
Two-dimensional Finite Element Model of Breast Cancer Cell Motion Through a Microfluidic Channel.
Jared Barber,Luoding Zhu +1 more
TL;DR: A two-dimensional model for red blood cell motion is adapted to consider the dynamics of breast cancer cells in a microfluidic channel and dynamics taking place when cells are near other objects are most sensitive to membrane and cytoplasm elasticity, and dynamics are significantly affected by low membrane bending elasticity.
Journal ArticleDOI
Low-frequency model-order reduction of electromagnetic fields without matrix factorization
TL;DR: A reduced-order modeling technique is developed, which is based on a low-frequency expansion of the electromagnetic field, which can be written in terms of the pseudoinverse of a so-called system matrix, and it is shown that it satisfies a reciprocity relation.
Book ChapterDOI
Accelerating nonsymmetrizable iterative methods
TL;DR: It is shown that the simplifications of Jea and Young (1983) can be used to derive three alternative forms of the Lanczos method, and a theoretical basis is given for choosing one of the forms in preference to the other two more frequently used forms.
References
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Journal ArticleDOI
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.
Journal ArticleDOI
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
TL;DR: In this article, a systematic method for finding the latent roots and principal axes of a matrix, without reducing the order of the matrix, has been proposed, which is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of minimized iterations.
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The principle of minimized iterations in the solution of the matrix eigenvalue problem
TL;DR: In this paper, an interpretation of Dr. Cornelius Lanczos' iteration method, which he has named ''minimized iterations'' is discussed, expounding the method as applied to the solution of the characteristic matrix equations both in homogeneous and nonhomogeneous form.
Journal ArticleDOI
Solution of Sparse Indefinite Systems of Linear Equations
TL;DR: The method of conjugate gradients for solving systems of linear equations with a symmetric positive definite matrix A is given as a logical development of the Lanczos algorithm for tridiagonalizing...
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