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ILL-POSED ALGEBRAIC EQUATION

by Peter C Chu, Leonid M. Ivanov, Y Y+y, Saa Sqy
"... signal Y noise Y’ Algebraic Equation L-dimensional state vector: a P-dimensional observation vector: Y ..."
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signal Y noise Y’ Algebraic Equation L-dimensional state vector: a P-dimensional observation vector: Y

SUNDIALS: Suite of Nonlinear and Differential/ Algebraic Equation Solvers

by Alan C. Hindmarsh, Peter N. Brown, Keith E. Grant, Steven L. Lee, Radu Serban, Dan E. Shumaker, Carol S. Woodward - ACM Trans. Math. Software , 2005
"... SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordi-nary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL, CVOD ..."
Abstract - Cited by 162 (6 self) - Add to MetaCart
SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordi-nary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL

Parallel Numerical Linear Algebra

by James W. Demmel, Michael T. Heath , Henk A. van der Vorst , 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
Abstract - Cited by 773 (23 self) - Add to MetaCart
We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We

Exact Solutions> Algebraic Equations and Systems of Algebraic Equations> Algebraic Equations> Algebraic Equation of General Form

by unknown authors
"... Algebraic equation of general form of degree n; the coefficients ak are real or complex numbers. 1◦. For brevity, denote the left-hand side of the equation, which is a polynomial of degree n, by Pn(x) = anxn + an−1xn−1 + · · · + a1x + a0 (an ≠ 0). (1) A number x = ξ is called a root of the equati ..."
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Algebraic equation of general form of degree n; the coefficients ak are real or complex numbers. 1◦. For brevity, denote the left-hand side of the equation, which is a polynomial of degree n, by Pn(x) = anxn + an−1xn−1 + · · · + a1x + a0 (an ≠ 0). (1) A number x = ξ is called a root

ALGEBRAIC EQUATIONS AND CONVEX BODIES

by Kiumars Kaveh, A. G. Khovanskii , 812
"... Dedicated to Oleg Yanovich Viro on the occasion of his sixtieth birthday Abstract. The well-known Bernstein-Kuˇshnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes. Recently the authors have found a far-reaching generalization of this theor ..."
Abstract - Cited by 6 (0 self) - Add to MetaCart
of this theorem to generic systems of algebraic equations on any quasi-projective variety. In the present note we review these results and their applications to algebraic geometry and convex geometry.

Parametrized Solutions of Algebraic Equations

by Franz Winkler - IMACS SC–93, LILLE FRANCE
"... In solving systems of algebraic equations we encounter basically two different situations. If the solution space is zero-dimensional we can list the finitely many solutions. This approach, however, fails if the dimension of the solution space is non-zero. We propose to use a parametrized representa ..."
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In solving systems of algebraic equations we encounter basically two different situations. If the solution space is zero-dimensional we can list the finitely many solutions. This approach, however, fails if the dimension of the solution space is non-zero. We propose to use a parametrized

Boundary Algebraic Equations for Lattice Problems

by P. G. Martinsson, G. J. Rodin - in IUTAM proceedings , 2002
"... Abstract. Boundary algebraic equations corresponding to Dirichlet boundary-value problems on lattices are introduced. These equations are based on the lattice Green’s function, from which dis-crete single- and double-layer potentials are derived. Structurally, the boundary algebraic equations are si ..."
Abstract - Cited by 9 (4 self) - Add to MetaCart
Abstract. Boundary algebraic equations corresponding to Dirichlet boundary-value problems on lattices are introduced. These equations are based on the lattice Green’s function, from which dis-crete single- and double-layer potentials are derived. Structurally, the boundary algebraic equations

Differential Algebraic Equations

by Luca Dede, Alfio Quarteroni, Luca Dede, Alfio Quarteroni , 2009
"... Parametrized systems of Differential Algebraic Equations (DAEs) stand at the base of several mathematical models in Microelectronics, Computational Fluid Dynamics and other Engineering fields. Since the dimension of these systems can be huge, high computational costs could occur, so efficient numeri ..."
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Parametrized systems of Differential Algebraic Equations (DAEs) stand at the base of several mathematical models in Microelectronics, Computational Fluid Dynamics and other Engineering fields. Since the dimension of these systems can be huge, high computational costs could occur, so efficient

Regularization of Differential-Algebraic Equations Revisited

by Michael Hanke - Preprint 92-19, Humboldt-Univ. Berlin, Fachbereich Mathematik , 1992
"... The present paper deals with quasilinear differential-algebraic equations with index 2. These equations are approximated by regularization methods. Such methods lead to singularly perturbed differential-algebraic equations. Using a geometric theory of singular perturbations convergence of the soluti ..."
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The present paper deals with quasilinear differential-algebraic equations with index 2. These equations are approximated by regularization methods. Such methods lead to singularly perturbed differential-algebraic equations. Using a geometric theory of singular perturbations convergence

LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares

by Christopher C. Paige, Michael A. Saunders - ACM Trans. Math. Software , 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax- b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
Abstract - Cited by 653 (21 self) - Add to MetaCart
-gradient algorithms, indicating that I~QR is the most reliable algorithm when A is ill-conditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmation--least squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebra--linear systems (direct and
Results 1 - 10 of 13,558