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The Conjugate Gradient Method for Solving Linear …

The Conjugate Gradient Method for SolvingLinear Systems of EquationsMike RamboMentor: Hans de MoorMay 2016 Department of Mathematics, Saint Mary s College of CaliforniaContents1 Introduction22 Relevant Definitions and Notation23 Linearization of Partial Differential Equations44 The Mechanisms of the Conjugate Gradient Steepest Descent .. Conjugate Directions .. Conjugate Gradient Method .. 145 Preconditioning186 Efficiency197 Conclusion208 References211 AbstractThe Conjugate Gradient Method is an iterative technique for Solving large sparse systems of linearequations. As a Linear algebra and matrix manipulation technique, it is a useful tool in approximatingsolutions to linearized partial differential equations .

2 Relevant De nitions and Notation Throughout this paper, the following de nitions and terminology will be utilized for the cg-method. De ntion 2.1.Partial Di erential Equations (PDEs): an equation in which the solution is a function which has two or more independent variables. Remark. The cg-method is utilized to estimate solutions to linear PDEs.

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