Search results for "iterointi"
showing 6 items of 6 documents
Yhtälöryhmän iteratiivinen ratkaiseminen
2015
Embracing iterations in Quantum software: a vision
2022
In today’s software engineering, iterations, affordable en masse, form an important part of just about any system. However, not all computing resources are cheap to consume. In High-Performance (HPC) and Quantum Computing (QC), executions can consume considerable amounts of energy and time, which is reserved and used even if the very first steps in the process fail. This means that developers must assume a different attitude towards programming, and aim at error-free software before its execution. This is com monly facilitated using simulators, which are commonplace for both HPC and QC. However the fashion developers advance from one tool to another is ad-hoc, with no established software e…
Evaluating a hierarchical approach to landscape level harvest scheduling
2018
Forest planning at the landscape level has the potential to become a large intractable problem. In Finland, Metsähallitus (the state enterprise that manages federally owned land) creates strategic plans to determine the appropriate harvest level. While these plans are feasible, they are not implementable in practice as the harvests are scattered temporally and spatially. Requiring that harvests be organized both temporally and spatially for practical implementation can result in an intractable problem. Through a hierarchical approach, the problem can be organized into steps in which the intractable problem is broken down into smaller easily solvable parts. As an approximation technique, the…
Numeeriset yhtälönratkaisumenetelmät
2017
Tämän tutkielman tavoitteena on käsitellä numeerisia yhtälönratkaisumenetelmiä matematiikan aineenopettajan näkökulmasta ja toimia lukion numeerisen matematiikan kurssin opettajan taustamateriaalina. Keskeinen sisältö käsittelee Lipschitz-jatkuvuutta, iteraatiota sekä Newton-Raphsonin menetelmää. Yhtälönratkaisu ja kahden lausekkeen yhtäsuuruuksien vertailu palautuu aina matematiikan klassiseen ongelmaan funktion nollakohdan etsimisestä. Keskeiset numeerisen yhtälönratkaisun metodit ovat rekursio ja iteraatio. Rekursio tarkoittaa oleellisesti toistoa. Iteraatiossa edellinen likiratkaisu ohjaa tarkentavasti seuraavan likiratkaisun laskentaa. Tällöin muodostuu tarkentuvien likiratkaisuiden lu…
Guaranteed error bounds for linear algebra problems and a class of Picard-Lindelöf iteration methods
2012
This study focuses on iteration methods based on the Banach fixed point theorem and a posteriori error estimates of Ostrowski. Their application for systems of linear simultaneous equations, bounded linear operators, as well as integral and differential equations is considered. The study presents a new version of the Picard–Lindelöf method for ordinary differential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of the approximation error. The estimates derived in the thesis take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations.