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Showing 1 to 14 of 14 for “"Ax = b"”.
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Optimum Semi-Iterative Methods for the Solution of Any Linear Algebraic System With a Square Matrix
… solution of a non-symmetric linear system, Ax = b, when the eigenvalues have positive real parts. The iterative parameters are reciprocals of the roots of a scaled and translated Chebyshev polynomial and depend upon an ellipse enclosing the spectrum of the system matrix.
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The Reconstruction of Binary Images in Discrete Tomography by Using the Binary Steering Scheme
… for solving an underdetermined linear system Ax = b. Three algorithms: Algebraic Reconstruction Technique (ART) Algorithm, Cimmino's Algorithm (CIM) with Equal Weights Algorithm and Fully-Simultaneous Diagonally-Relaxed Orthogonal Projections (DROP) Algorithm are modified. We develop an …
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Polynomial Preconditioning for Conjugate Gradient Methods
The solution of a linear system of equations, Ax = b, arises in many scientific applications. If A is large and sparse, an iterative method is required. When A is hermitian positive definite (hpd), the conjugate gradient method of Hestenes and Stiefel is popular. When A is hermitian indefinite …
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Preconditioned iterative methods for highly sparse, nonsymmetric, unstructured linear algebra problems
… the solution of a system of linear equations Ax = b in which A is large, highly sparse, nonsymmetric, and unstructured. Several iterative methods which are applicable to nonsymmetric and indefinite problems are applied to a suite of test problems derived from simulations of actual bipolar …
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Incomplete factorization preconditioning for linear least squares problems
… sparse linear least squares problems, $min\Vert Ax-b\Vert\sb2$, is proposed. The family is based on incomplete Gram-Schmidt (IGS) factorizations of A. Particular attention has been given to the following members of the family: Incomplete Classical Gram-Schmidt (ICGS), Incomplete Modified …
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Vanishing and non-vanishing of L-series of elliptic curves twisted by Dirichlet characters
… L -series of an elliptic curve E : y 2 = x 3 + Ax + B with A, B ✹ [Special characters omitted.] . If there exists a cyclic cubic character { such that L ( E , 1, {) = 0 or if L ( E , 1) = 0 then the L -series vanishes for an infinite number of cyclic cubic characters. With finite exceptions, if …
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High-Performancs Sparse Matrix-Vector Multiplication on GPUS for Structured Grid Computations
… With uniform grids, the resulting linear system Ax = b has a matrix A that is sparse with a very regular structure. The specific focus of this thesis is on sparse matrices that have a block structure due to the large number of unknowns at each grid point. Sparse matrix storage formats such as …
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Potensi bakteri Enterobacter agglomerans sebagai biosorben logam berat timbal (Pb)
… panjang gelombang 600 nm menggunakan persamaan y=ax+b. Pengamatan pertumbuhan bakteri dengan konsentrasi logam berat timbal 0, 5, 10, 15 dan 20 ppm dihitung dengan melihat nilai OD setiap 4 jam sampai 28 jam, pada puncak fase log data dianalisis dengan ANOVA progam SPSS 16. Untuk mengetahui …
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Matrix Factorizations, Triadic Matrices, and Modified Cholesky Factorizations for Optimization
… is computed by solving a linear symmetric system Ax=b. When A is not positive definite, the computed search direction may not be a descent direction. Modified Newton methods add a perturbation E to A, so that A+E is positive definite, where E is symmetric positive semidefinite. We study the …
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Computational Experience with Linear Optimization and Related Problems
… in practice for linear systems (i.e., solving Ax = b, where A is an n x n matrix with full-rank and b is an n-vector) is not a solution to the underlying problem of scaling a linear program. A small computational study depicts the effectiveness of the Orchard-Hays triangularization technique in …
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Invariant tests for scale parameters under elliptical symmetry
… x has a spherical law, then the distribution of Ax + b is said to be elliptically symmetric. The class of spherically symmetric laws contains such heavy-tailed distributions as the spherical Cauchy law and other symmetric stable distributions. As such laws need not have moments, the emphasis here …
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Velocity and Q from reflection seismic data
… in a system of linear equations of the form AX = B, with A the design matrix, X the solution vector, and B the data vector. The system of normal equations is AᵀAX = AᵀB where the least-squares estimate of X = X = V(1/S)UᵀB and the SVD of A is A = USVᵀ. A technique to improve the sparsity …
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El método de Neville : un enfoque basado en computación de altas prestaciones
… Neville sobre un sistema de ecuaciones lineales (Ax=b) en un computador paralelo, utilizando el paradigma de paso de mensajes y distintas métricas que nos han permitido analizar las prestaciones de los algoritmos estudiados. La eliminación de Neville es un procedimiento alternativo a la …
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Efficient projection space updates for the approximation of iterative solutions to linear systems with successive right hand sides
Accurate initial guesses to the solution can dramatically speed convergence of iterative solvers. In the case of successive right hand sides, it has been shown that accurate initial solutions may be obtained by projecting the newest right hand side vector onto a column space of recent prior …