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Preconditioner - Wikipedia

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In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by an iterative method. In linear algebra and numerical analysis, a preconditioner 𝑃 of a matrix 𝐴 is a matrix such that 𝑃 − 1 𝐴 has a smaller condition number than 𝐴 . It is also common to call 𝑇 = 𝑃 − 1 the preconditioner, rather than 𝑃 , since 𝑃 itself is rarely explicitly available. In modern preconditioning, the application of 𝑇 = 𝑃 − 1 , i.e., multiplication of a column vector, or a block of column vectors, by 𝑇 = 𝑃 − 1 , is commonly performed in a matrix-free fashion, i.e., where neither 𝑃 , nor 𝑇 = 𝑃 − 1 (and often not even 𝐴 ) are explicitly available in a matrix form. Preconditioners are useful in iterative methods to

Preconditioner - Wikipedia Jump to content From Wikipedia, the free encyclopedia Transforms equations for numerical solution "Preconditioning" redirects here. For other uses, see Preconditioning (disambiguation) . This article includes a list of general references but lacks corresponding inline citations . Please help improve this article by introducing more precise citations. ( February 2013 ) ( Learn how and when to remove this message ) In mathematics , preconditioning is the application of a transformation, called the preconditioner , that conditions a given problem into a form that is mor

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