Conjugate Gradient Type Methods for Ill-Posed Problems (Pitman Research Notes in Mathematics Series)

Sprache: Englisch

Verlag: Longman, 1995

0582273706 / 9780582273702

Serie: Buch 16 von 39 - Chapman & Hall/CRC Research Notes in Mathematics

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Paperback, x + 134 pages, NOT ex-library. Good condition, faint staining to lower edges, gently bent lower outer corners; unmarked text, free of inscriptions and stamps. -- This monograph provides a detailed examination of conjugate gradient type methods and their application to linear ill-posed problems, focusing on their effectiveness as regularisation tools. Such problems, which lack continuous dependence on the data and often require careful handling of noise and incompleteness, appear throughout the natural and technical sciences. Examples include astronomical and geophysical imaging, signal analysis, computerised tomography and inverse heat transfer. The text presents a unifying analysis covering a family of these iterative methods, among them minimal residual approaches and the classical conjugate gradient algorithm. It explores their regularising properties in depth, establishes sharp convergence results and discusses practical aspects such as the selection of stopping rules. The analytical framework relies on the close connection between conjugate gradient iterations and the theory of real orthogonal polynomials, supplying the necessary background in an opening section. Building on foundational contributions, including those of Nemirovskii, the book makes available results that were previously scattered or published mainly in Russian, and introduces new techniques particularly for the Hestenes-Stiefel variant. Extensions to self-adjoint indefinite operator equations are also addressed. Numerical illustrations for image reconstruction and inverse heat transfer demonstrate the methods' performance in concrete settings. With the growing importance of inverse problems in contemporary fields such as medical imaging, remote sensing, machine learning regularisation and geophysical data inversion, this work offers enduring theoretical foundations for the design of stable computational algorithms. It serves as a useful reference for mathematicians, engineers and scientists engaged in developing or applying iterative solutions to unstable inverse problems in high-dimensional or noisy environments. …

Bestandsnummer des Verkäufers 013347

Titel
Conjugate Gradient Type Methods for Ill-Posed Problems (Pitman Research Notes in Mathematics Series)
Autor
Martin Hanke
Verlag
Longman
Erscheinungsjahr
1995
Zustand
Good
Einband
Soft cover
Sprache
Englisch
ISBN-10
0582273706
ISBN-13
9780582273702
Auflage
1st Edition
Serie
Buch 16 von 39: Chapman & Hall/CRC Research Notes in Mathematics

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All U.S.-bound orders are now shipped with UPS for reliable delivery. Additional customs or import fees are highly unlikely; however, please note buyers remain responsible for any duties or taxes that U.S. Customs may assess. -- Killarneybooks is a family-run bookshop based in the Republic of Ireland. We take pride in accurate listings, careful packaging, and prompt service - most orders ship within 24 hours. All books listed are in stock and ready for immediate dispatch - we are not dropshippers. Inquiries always welcome.…

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