Least-Change Sparse Secant Update Methods with Inaccurate Secant Conditions
نویسندگان
چکیده
منابع مشابه
A new gradient method via least change secant update
The Barzilai–Borwein (BB) gradient method is favourable over the classical steepest descent method both in theory and in real computations. This method takes a 'fixed' step size rather than following a set of line search rules to ensure convergence. Along this line, we present a new approach for the two-point approximation to the quasi-Newton equation within the BB framework on the basis of a w...
متن کاملOn the Relation between Two Local Convergence Theories of Least-change Secant Update Methods
In this paper, we show that the main results of the local convergence theory for least-change secant update methods of Dennis and Walker (SIAM J. Numer. Anal. 18 (1981), 949-987) can be proved using the theory introduced recently by Martinez (Math. Comp. 55 (1990), 143-167). In addition, we exhibit two generalizations of well-known methods whose local convergence can be easily proved using Mart...
متن کاملAn All-Inclusive Efficient Region of Updates for Least Change Secant Methods
Least change secant methods, for function minimization, depend on nding a \good" symmetric positive deenite update to approximate the Hessian. This update contains new curvature information while simultaneously preserving, as much as possible, the built up information from the previous update. Updates are generally derived using measures of least change based on some function of the eigen-value...
متن کاملSecant methods for semismooth equations
Some generalizations of the secant method to semismooth equations are presented. In the one-dimensional case the superlinear convergence of the classical secant method for general semismooth equations is proved. Moreover a new quadratically convergent method is proposed that requires two function values per iteration. For the n-dimensional cases, we discuss secant methods for two classes of com...
متن کاملConvergence Conditions for the Secant Method
We provide new sufficient convergence conditions for the convergence of the Secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, Lipschitz–type and center–Lipschitz–type instead of just Lipschitz–type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 1985
ISSN: 0036-1429,1095-7170
DOI: 10.1137/0722046