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On Approximation of Equations by Algebraic Equations
Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, 1964Some years ago D. I. Muller [1] developed a method for the solution of algebraic equations, approximating them by quadratic equations. The method proved extremely efficient in many tests. However, the theoretical discussion given by Muller can hardly be considered as adequate, in my opinion, as his convergence proof culminates in a vicious circle (cf ...
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1987
Many important problems in science and engineering require the solution of systems of simultaneous linear equations of the form $$\begin{gathered} a_{11} x_1 + a_{12} x_2 + \cdots + a_{1n} x_n = b_1 \hfill \\ a_{21} x_1 + a_{22} x_2 + \cdots + a_{2n} x_n = b_2 \hfill \\ \,\,\,\,.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,
Ian Jacques, Colin Judd
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Many important problems in science and engineering require the solution of systems of simultaneous linear equations of the form $$\begin{gathered} a_{11} x_1 + a_{12} x_2 + \cdots + a_{1n} x_n = b_1 \hfill \\ a_{21} x_1 + a_{22} x_2 + \cdots + a_{2n} x_n = b_2 \hfill \\ \,\,\,\,.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,
Ian Jacques, Colin Judd
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Differential Algebraic Equations
2012In Chaps. 2 and 3 we were concerned mainly with the numerical solution of ordinary differential equations of the form y′ = f(x, y). However, there are problems which are more general than this and require special methods for their solution. One such class of problems are differential algebraic equations (DAEs).
Karline Soetaert +2 more
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Differential-Algebraic Equations
Oberwolfach Reports, 2007The topic of Differential Algebraic Equations (DAEs) began to attract significant research interest in applied and numerical mathematics in the early 1980's. Today, a quarter of a century later, DAEs are an independent field of research, which is gaining in importance and becoming of increasing interest for both applications and mathematical theory.
Stephen L. Campbell +3 more
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Differential — Algebraic Equations
2003Differential — algebraic equations (DAE) differ from other problems with solutions given by smooth and continuous parametric sets. They combine specifics of the nonlinear algebraic or transcendental equations with those of ODE. Correct formulation of the Cauchy problem for such equations requires solution of a system of nonlinear equations.
V. I. Shalashilin, E. B. Kuznetsov
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Differential Algebraic Equations
2017This chapter documents how to formulate and solve optimization problems with differential and algebraic equations (DAEs). The pyomo.dae package allows users to easily incorporate detailed dynamic models within an optimization framework and is flexible enough to represent a wide variety of differential equations.
William E. Hart +6 more
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1995
Abstract This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions.
Peter Lancaster, Leiba Rodman
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Abstract This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions.
Peter Lancaster, Leiba Rodman
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Soviet Physics Journal, 1977
A generalization of the theory of algebraic properties is proposed for an equation of general form, providing a tool for the acquisition of new results with regard to the symmetry of certain nondifferential equations of theoretical physics.
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A generalization of the theory of algebraic properties is proposed for an equation of general form, providing a tool for the acquisition of new results with regard to the symmetry of certain nondifferential equations of theoretical physics.
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Continuous-time distributed algorithms for solving linear algebraic equation
Cybersecurity and Cyberforensics Conference, 2017Kai Cao, Xianlin Zeng, Yiguang Hong
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2018
The aim of this chapter is to show how equations of degrees less than 5 can be solved. We highlight well-known formulae for the quadratic equation and show how to find similar formulae for cubic and quartic equations. We also explain why as early as the eighteenth century mathematicians started to doubt the possibility to find solutions for general ...
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The aim of this chapter is to show how equations of degrees less than 5 can be solved. We highlight well-known formulae for the quadratic equation and show how to find similar formulae for cubic and quartic equations. We also explain why as early as the eighteenth century mathematicians started to doubt the possibility to find solutions for general ...
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