<電子ブック>
Numerical Derivatives and Nonlinear Analysis / by Harriet Kagiwada, Robert Kalaba, Nima Rasakhoo, Karl Spingarn
(Mathematical Concepts and Methods in Science and Engineering ; 31)
版 | 1st ed. 1986. |
---|---|
出版者 | (New York, NY : Springer US : Imprint: Springer) |
出版年 | 1986 |
本文言語 | 英語 |
大きさ | 212 p : online resource |
著者標目 | *Kagiwada, Harriet author Kalaba, Robert author Rasakhoo, Nima author Spingarn, Karl author SpringerLink (Online service) |
件 名 | LCSH:Electrical engineering LCSH:Computer science FREE:Electrical and Electronic Engineering FREE:Computer Science |
一般注記 | 1. Methods for Numerical Differentiation -- 1.1. Wengert’s Method -- 1.2. FEED (Fast and Efficient Evaluation of Derivatives) -- 1.3. An Implementation of the FEED Procedure in BASIC -- 1.4. Wexler’s Approach -- 1.5. Higher-Order Methods for Finding Roots -- Exercises -- 2. Nonlinear Least Squares -- 2.1. Fitting the CES Production Function -- 2.2. Passive Ranging -- 2.3. Constrained Optimization -- 3. Optimal Control -- 3.1. Control Theory -- 3.2. Numerical Methods -- 3.3. Description of the Subroutines -- 3.4. Examples of Optimal Control Problems -- 3.5. Program Listings -- Exercises -- 4. System Identification -- 4.1. Quasilinearization -- 4.2. Fast and Efficient Evaluation of Derivatives (FEED) -- 4.3. Computer Program -- 4.4. Numerical Results -- 4.5. Program Listing -- 5. Sukhanov’s Variable Initial Value Method for Boundary Value Problems -- 5.1. Sukhanov’s Initial Value Equations -- 5.2. Automatic Derivative Evaluation -- 5.3. Examples Using Sukhanov’s Method -- 5.4. Program Listing -- Exercises -- 6. Nonlinear Integral Equations -- 6.1. Derivation of the Imbedding Equations -- 6.2. Method of Computation -- 6.3. Automatic Derivative Evaluation -- 6.4. Examples of Integral Equation Problems -- 6.5. Program Listing -- Exercises -- References -- Author Index For many years it has been an article of faith of numerical analysts that the evaluation of derivatives of complicated functions should be avoided. Derivatives were evaluated using finite differences or, more recently, using symbolic manipulation packages. The first has the disadvantage of limited accuracy. The second has disadvantages of being expensive and requiring considerable computer memory. The recent developments described in this text allow the evaluation of derivatives using simple automatic derivative evaluation subroutines pro grammed in FORTRAN or BASIC. These subroutines can even be programmed on a personal computer. The concept for the evaluation of the derivatives was originally developed by Wengert over 20 years ago. Significant im provements have been made in Wengert's method and are utilized in this text. The purpose of this text is to familiarize computer users with a simple and practical method for obtaining the partial derivatives of complicated mathematical expressions. The text illustrates the use of automatic deriva tive evaluation subroutines to solve a wide range of nonlinear least-squares, optimal control, system identification, two-point boundary value problems, and integral equations. The numerical values of the derivatives are evalu~ ated exactly, except for roundoff, using simple FORTRAN or BASIC sub routines. These derivatives are derived automatically behind the scenes, from the equivalent of analytical expressions, without any effort from the user. The use of costly software packages is not required HTTP:URL=https://doi.org/10.1007/978-1-4684-5056-9 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9781468450569 |
|
電子リソース |
|
EB00233733 |
類似資料
この資料の利用統計
このページへのアクセス回数:6回
※2017年9月4日以降