منابع مشابه
Multiple zeros of nonlinear systems
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Finding approximate solutions to systems of n nonlinear equations in n real variables is a much studied problem in numerical analysis. Somewhat more recently, researchers have developed numerical methods to provide mathematically rigorous error bounds on such solutions. (We say that we “verify” existence of the solution within those bounds on the variables.) However, when the Jacobi matrix is s...
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Abstract. Traditional computational fixed point theorems, such as the Kantorovich theorem (made rigorous with directed roundings), Krawczyk’s method, or interval Newton methods use a computer’s floating-point hardware computations to mathematically prove existence and uniqueness of a solution to a nonlinear system of equations within a given region of n-space. Such computations require the Jaco...
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Computational fixed point theorems can be used to automatically verify existence and uniqueness of a solution to a nonlinear system of equations F (x) = 0, F : R n → R n within a given region x of n-space. But such computations succeed only when the Jacobi matrix F (x) is nonsingular everywhere in x. However, in many practical problems, the Jacobi matrix is singular, or nearly so, at the soluti...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2011
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2011-02462-2