Accession Number:

ADA093608

Title:

An Updated Version of the Kantorovich Theorem for Newton's Method.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

• Miel,George

Report Date:

1980-10-01

Pagination or Media Count:

17.0

Abstract:

An affine invariant version of the Kantorovich theorem for Newtons method is presented. The result includes the Gragg-Tapia error bounds, as well as recent optimal and sharper upper bounds, new optimal and sharper lower bounds, and new inequalities showing q-quadratic convergence all in terms of the usual majorizing sequence. Closed form expressions for these bounds are given. Author

Descriptors:

• *NUMERICAL ANALYSIS
• *BOUNDARIES
• *ERROR ANALYSIS
• CONVERGENCE
• SCALAR FUNCTIONS
• NONLINEAR ANALYSIS
• ITERATIONS
• SEQUENCES(MATHEMATICS)
• THEOREMS
• BANACH SPACE

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE