Point estimation of root finding methods / Miodrag Petković.

Format:

Book

Author/Creator:

Petković, Miodrag.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 1933.

Lecture notes in mathematics, 0075-8434 ; 1933

Language:

English

Subjects (All):

Fix-point estimation.

Equations, Roots of.

Physical Description:

xii, 210 pages : illustrations ; 24 cm.

Place of Publication:

Berlin : Springer, [2008]

Contents:

1.1 Simultaneous Methods for Finding Polynomial Zeros 1

1.2 Localization of Polynomial Zeros 26

1.3 Complex Interval Arithmetic 32

2 Iterative Processes and Point Estimation Theory 35

2.1 Newton's Method Estimates 35

2.2 Approximate Zeros of Quadratically Convergent Methods 44

2.3 Approximate Zeros of Higher-Order Methods 48

2.4 Improvement of Smale's Result 51

2.5 Point Estimation of Durand-Kerner's Method 59

3 Point Estimation of Simultaneous Methods 67

3.1 Point Estimation and Polynomial Equations 67

3.2 Guaranteed Convergence: Correction Approach 71

3.3 Guaranteed Convergence: Sequence Approach 97

3.4 A Posteriori Error Bound Methods 118

4 Families of Simultaneous Methods of Higher Order: Part I 129

4.1 Hansen-Patrick's Family of Root Finding Methods 129

4.2 Derivative-Free Family of Simultaneous Methods 132

4.3 Family of Simultaneous Methods with Derivatives 146

4.4 Numerical Examples 156

5 Families of Simultaneous Methods of Higher Order: Part II 161

5.1 One-Parameter Family for Simple Zeros 161

5.2 Family of Methods with Corrections 174

5.3 Family of Interval Methods 186.

Notes:

Includes bibliographical references (pages 197-204) and index.

ISBN:

3540778500

9783540778509

OCLC:

213479424