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IMPLEMENTATION ISSUES FOR HIGH-ORDER ALGORITHMS

JEAN-PIERRE DUSSAULT, BENOIT HAMELIN, BILEL KCHOUK

Abstract

Newton-Raphson method, which dates back to 1669–1670, is widely used to solve systems of equations and unconstrained optimization problems. Newton-Raphson consists in linearizing the system of equations and provides quadratic local convergence order. Quite soon after Newton and Raphson introduced their iterative process, Halley in 1694 proposed a higherorder method providing cubic asymptotic convergence order. Chebyshev in 1838 proposed another high-order variant. In High-order Newton-penalty Algorithms [2], by interpreting Newton’s iteration as a linear extrapolation, formulæ were proposed to compute higher-order extrapolations generalizing Newton-Raphson’s and Chebyshev’s methods.

In this paper, we provide details using an automatic differentiation (AD) tool to implement those high-order extrapolations. We present a complexity analysis allowing to predict the efficiency of those high-order strategies.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
Lịch hoạt động chung Lịch sử dụng phòng, hội trường, hội thảo Ảnh hoạt động
Giới thiệu Đăng nhập Đăng ký tài khoản Quên mật khẩu Chính sách bảo mật
Messages2TimelineExceptionsViews8RouteQueries108Models431MailsGateSessionRequest
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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