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Displaying similar documents to “Matrix transformations and quasi-Newton methods.”

Some notes on the quasi-Newton methods

Masanori Ozawa, Hiroshi Yanai (1982)

Aplikace matematiky

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A survey note whose aim is to establish the heuristics and natural relations in a class of Quasi-Newton methods in optimization problems. It is shown that a particular algorithm of the class is specified by characcterizing some parameters (scalars and matrices) in a general solution of a matrix equation.

A Newton-Kantorovich-SOR type theorem

Béla Finta (2005)

Open Mathematics

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In this paper we propose a new method for solving nonlinear systems of equations in finite dimensional spaces, combining the Newton-Raphson's method with the SOR idea. For the proof we adapt Kantorovich's demonstration given for the Newton-Raphson's method. As applications we reobtain the classical Newton-Raphson's method and the author's Newton-Kantorovich-Seidel type result.