Sökning: "infinite-dimensional"

Visar resultat 1 - 5 av 8 uppsatser innehållade ordet infinite-dimensional.

  1. 1. Kernel Methods for Regression

    Kandidat-uppsats, Linnéuniversitetet/Institutionen för matematik (MA)

    Författare :Tom Lennart Rossmann; [2023]
    Nyckelord :Kernel Methods; Regression; Ridge Regression;

    Sammanfattning : Kernel methods are a well-studied approach for addressing regression problems by implicitly mapping input variables into possibly infinite-dimensional feature spaces, particularly in cases where standard linear regression fails to capture non-linear relationships in data. Therefore, the choice between standard linear regression and kernel regression can be seen as a tradeoff between constraints on the number of features and the number of training samples. LÄS MER

  3. 2. Erdős-Kaplansky Satsen

    Kandidat-uppsats, Uppsala universitet/Algebra, logik och representationsteori

    Författare :Edvin Lundin; [2023]
    Nyckelord :dualspace; cardinality; dimension; infinite-dimensional; vectorspace; dualrum; kardinalitet; dimension; oändlig-dimensionell; oändlig-dimensionella; vektorrum;

    Sammanfattning : Inom linja ̈r algebra har varje vektorrum ett s ̊a kallat dualrum, vilket är ett vektorrum bestående av alla linjära funktioner från det ursprungliga rummet till sin kropp. Att beräkna dimensionen av ett dualrum tillhörande ett ändlig-dimensionellt vektorrum är relativt enkelt, för oändlig-dimensionella vektorrum är det mer komplicerat. LÄS MER

  4. 3. On Levi Decompositions in Finite and Infinite Dimensional Lie Algebras

    Kandidat-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Författare :Hannes Nilsson; [2021]
    Nyckelord :Lie algebra; Levi s theorem; Cohomology; Virasoro algebra; Mathematics and Statistics;

    Sammanfattning : In this bachelor thesis we introduce Lie algebras, and use Lie algebra cohomology to prove Levi's theorem about splitting of finite dimensional Lie algebras. We then construct the Virasoro algebra, compute its low dimensional cohomology spaces, and use this to demonstrate why Levi's theorem does not hold in the infinite dimensional case... LÄS MER

  5. 4. Cubature on Wiener Space for the Heath--Jarrow--Morton framework

    Master-uppsats, Mälardalens högskola/Akademin för utbildning, kultur och kommunikation

    Författare :Lutufyo Mwangota; [2019]
    Nyckelord :Heath–Jarrow–Morton model; stochastic Taylor expansion; Cubature formulae; Brownian signature; forward rate.;

    Sammanfattning : This thesis established the cubature method developed by Gyurkó & Lyons (2010) and Lyons & Victor (2004) for the Heath–Jarrow–Morton (HJM) model. The HJM model was first proposed by Heath, Jarrow, and Morton (1992) to model the evolution of interest rates through the dynamics of the forward rate curve. LÄS MER

  7. 5. Comparative Study of Several Bases in Functional Analysis

    Kandidat-uppsats, Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Författare :Maria Miranda Navarro; [2018]
    Nyckelord :Banach space; Hilbert space; Hamel basis; Schauder basis; Orthonormal basis;

    Sammanfattning : From the beginning of the study of spaces in functional analysis, bases have been an indispensable tool for operating with vectors and functions over a concrete space. Bases can be organized by types, depending on their properties. This thesis is intended to give an overview of some bases and their relations. LÄS MER