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Showing 1 to 20 of 21 for “"Gaussian Elimination"”.
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Smoothed analysis of Gaussian elimination
We present a smoothed analysis of Gaussian elimination, both with partial pivoting and without pivoting. Let A be any matrix and let A be a slight random perturbation of A. We prove that it is unlikely that A has large condition number. Using this result, we prove it is unlikely that A has large …
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A comparison of parallel Gaussian elimination solvers for the computation of electrochemical battery models on the cell processor
… In particular, three different banded parallel Gaussian elimination solvers are developed and compared. These three solvers vividly illustrate how performance achieved on the new multicore processors is strongly dependent on the algorithm used.
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Preconditioning For Matrix Computation
… way we support application of GENP, that is, Gaussian elimination with no pivoting, and block Gaussian elimination. We prove that the proposed preconditioning methods are efficient when we apply Gaussian random matrices as preconditioners. We confirm these results with our extensive numerical …
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A hybrid direct-iterative linear solver for chemical process simulation
… of direct sparse linear methods (e.g., Gaussian elimination) with the efficiency of iterative sparse linear methods (e.g., Krylov subspace methods). The new hybrid solver is implemented in the SEQUEL-II, ASPEN PLUS$\sp{\rm TM}$, and SPEEDUP$\sp{\rm TM}$ programs and evaluated in terms of …
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Global Optimization in Least Squares Problems in FTIR Spectroscopy and X -Ray Crystallography
… of linear equations for which we develop a fast Gaussian elimination algorithm. For noncentrosymmetric structures, we reduce the phase problem to a mixed-integer quadratic problem and utilize a branch-and-bound algorithm for its solution."
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Estruturas tridimensionais com propriedades mecânicas dos materiais representadas matematicamente por séries - aplicação à análise de pontes
… system of linear equations is obtained by the Gaussian elimination method, employing a block solver. A computer program is presented and applied to some examples.
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Comparison of energy minimization with direct stiffness for linear structural analysis
… being analyzed. These equations are solved by Gaussian elimination to determine the generalized displacement vector. Computer codes have been written for the energy minimization and direct stiffness methods. The comparison was based on computational effort, in terms of computer time, required …
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APPROXIMATE GROBNER BASES A BACKWARDS APPROACH
… avoid the strict monomial orderings and ordered elimination (reduction) strategies, at the heart of Buchberger-type methods, which are usually numerically unstable. For the the computation of exact bases for an ideal near to the one from which we began, we make avid use of structured (numerical) …
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A Multigrid Acceleration for an ADI Finite Difference Method for Two-Dimensional Space Fractional Diffusion Equations
… as the regular finite difference method with Gaussian elimination. Our preliminary numerical examples run for two dimensional model problem of intermediate size seem to indicate the observations: To achieve the same accuracy, the new method has a significant reduction of the CPU time from more …
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An Adaptive Educational Game To Help Students Learn How To Solve Systems Of Linear Equations
… for linear equations that adopts the rules of Gaussian Elimination. The student module records the student's performance and provides the pedagogical module with the required information about the student's current skills. The pedagogical module uses the automated solver to assess the student's …
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Exploiting compression in solving discretized linear systems
… linear systems, including direct methods such as Gaussian elimination and iterative methods such as GMRES. This thesis proposes a method for exploiting compression while computing the solution to a given discretized system of linear algebraic equations and investigates both its overall …
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Making Hybrid Systems Easier to Model, Simulate, and Visualize
… (BTA), program differentiation, symbolic Gaussian elimination, and abstract interpretation using interval analysis. We give an operational semantics for the specialization process along with a declarative and algorithmic specifications of the binding-time analysis. A type safety theorem is …
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Dynamic response of the supercritical C0₂ Brayton recompression cycle to various system transients
… a semi-implicit solution process and implements Gaussian elimination to solve the system of equations. Transient behavior of the printed circuit heat exchangers is determined via the previously developed code HXMOD. Turbomachinery performance is modeled using the Real Gas Radial Compressor (RGRC) …
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An F4-Style Involutive Basis Algorithm
… echelon form of this system will be obtained by Gaussian elimination then give us the solution. Similarly, Gröbner Basis is the “nice form” of nonlinear equation systems that can span all the polynomials in the given ideal [4]. So we can use Gröbner Basis to analyze the solution of a nonlinear …
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Numerical solution for the submerged pulsating line source in the presence of a free surface
… identity were solved by using IMSL routines for Gaussian Elimination, and the behavior of the influence coefficient matrix was tested by using LINPACK routines. The depth of the submerged-source and wave number was kept constant while the length of near field and the number of panels per …
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Implementation of Instantaneous Frequency Estimation based on Time-Varying AR Modeling
… equations. Conventional approaches such as Gaussian elimination or direct matrix inversion are computationally inefficient for solving such a system of equations especially when the covariance matrix has a high order. We implement two recursive algorithms for efficiently inverting the …
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Symbolic-numeric algorithms for simplifying differential systems and their application to the determination of approximate Lie symmetry algebras
… integrability conditions. Differential elimination methods can be applied to these systems, which involve a finite number of differentiations and eliminations to reveal hidden constraints, and form the determining equations of symmetries. Normally, such PDE systems have approximate …
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A Structure-based Attack on the Linearized Braid Group-based Diffie-Hellman Conjugacy Problem in Combination with an Attack using Polynomial Interpolation and the Chinese Remainder Theorem
… attack is to use an algorithm that combines Gaussian elimination with integer polynomial interpolation and the Chinese remainder theorem (CRT), instead of fast matrix multiplication as suggested by others. The major idea here is to distribute the task of solving a system of linear equations …
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Polynomial identity testing of read-once oblivious algebraic branching programs
… show how it can be used as a form of oblivious Gaussian elimination. As an application, we strengthen a result of Mulmuley [Mul12a], and show that derandomizing a particular case of the Noether Normalization Lemma is reducible to black-box PIT of read-once oblivious ABPs. Using our hitting set …
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Stability of the Bruhat decomposition
… in the derived matrices. For example, for Gaussian elimination with partial pivoting (GEPP), the growth of elements in the derived matrices is measured using the growth factor YoP = maxla;~I/ maxia;,I, where A(i) = [a;n is the ith l,J,I; J,k derived matrix. GEPP is well-known to be unstable …
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