The effect of new Stokes curves in the exact steepest descent method
نویسندگان
چکیده
The exact steepest descent method was born in [AKT4] by combining the ordinary steepest descent method with the exact WKB analysis. (See, e.g., [AKT2] for the notion and notations of the exact WKB analysis used in this report.) It is a straightforward generalization of the ordinary steepest descent method and provides us with a new powerful tool for the description of Stokes curves as well as for connection problems of ordinary differential equations. Still in [AKT4] some restrictions were imposed for its applicability. In this report, in order that we may remove such restrictions and apply it to more general equations in the future, we discuss the effects of several kinds of new Stokes curves in the exact steepest descent method. Let us here review the exact steepest descent method briefly. An equation to be discussed is an ordinary differential equation with polynomial coefficients of the following form:
منابع مشابه
A new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations
In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...
متن کاملA Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems
In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...
متن کاملOn global aspects of exact WKB analysis of operators admitting infinitely many phases
A case-study of the Stokes geometry in the large is given for some concrete examples of WKB type operators that admit infinitely many phases. In all the examples discussed in this article virtual turning points and new Stokes curves emanating from them neatly resolve the trouble we encounter. Some computerassisted study of the configuration of the steepest descent paths is employed to show that...
متن کاملHybrid steepest-descent method with sequential and functional errors in Banach space
Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...
متن کامل