In general, when a quasi-Newton method is applied to solve a system of nonlinear equations, the quasi-Newton direction is not necessarily a descent direction for the norm function. In this paper, we ...
SIAM Journal on Numerical Analysis, Vol. 42, No. 5 (2005), pp. 1830-1845 (16 pages) The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method for discretized ...
This book serves as a bridge between graduate textbooks and research articles in the area of nonlinear elliptic partial differential equations. Whereas graduate textbooks present basic concepts, the ...
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