3 research outputs found

    Reverse accumulation and implicit functions

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    Original article can be found at: http://www.informaworld.com/smpp/title~content=t713645924~db=all Copyright Taylor and Francis / Informa.We begin by introducing a simple technique for using reverse accumulation the first derivatives of target functions which include in their construction the solution of systems of linear or nonlinear equations. In the linear case solving Ay= b for y corresponds to the adjoint operations [...] where vis the solution to the adjoint equations vA=y. A more sophisticated construction applies in the nonlinear case. We apply these technique to obtain automatic numerical error estimates for calculated function values. These error estimates include the effects of inaccurate equation solution as well as rounding error. Our basic techniques can be generalized to functions which contain several (linear or nonlinear) implicit functions in their construction, either serially or nested. In the case of scalar-valued target functions that include equation solution as part of their construction. Our algorithms involve at most the same order of computational effort as the computation of the target function value, regardless of the number of independent variables or the size of the systems of equations.Peer reviewe

    Whakaora ngā Whenua Whāma: Utilising mātauranga Māori and Western science to protect and restore the soil on rural farms in Te Tai Tokerau

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    Māuranga Māori [Māori knowledge] Before the arrival of the European settlers, Māori society was governed by a system of principles, laws, and customs known as tikanga Māori. The terminology, tikanga, is derived from the word tika that means to be righteous, honest, and just. At the heart of mātauranga Māori is tikanga and both principles conceptualise whakawhanaungatanga (making good kin relationships) and whakapapa (shared ancestry). Through whanaungatanga (kin relations), a Māori world, both visible and invisible, is conceptualised and apprehended as palpable. Conceptually, whakapapa can be understood as the interminable connections from the Atua (Māori gods) to earth to the people. Whakapapa binds Māori people together in a sacred relationship and responsibility to care for each other, the soil, air, and water. Prior to colonisation, mātauranga Māori that included the principles of tika, tikanga Māori, whakawhanaungatanga, whanaungatanga, and whakapapa enabled Māori to live a tika (good, just, decent) life. Since the beginning of colonisation of Aotearoa New Zealand, by the British, kāinga have been damaged by the scientific, calculative, logical discourse. Through the dominant English language and culture, the Māori people have been pressured to obey linguistic conventions which are distinctly Western. In the Whenua Whāma project, the research team has begun to talk deeply of a cultural interface that draws attention to Māori beliefs, interaction, and self-development in the areas of organic and regenerative agriculture across Te Tai Tokerau, Aotearoa
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