Essays about: "tensor product"

Showing result 1 - 5 of 14 essays containing the words tensor product.

  1. 1. On quantum systems and the measurement problem

    University essay from Stockholms universitet/Fysikum

    Author : Nicolas Boulle; [2023]
    Keywords : Quantum physics; the measurement problem; quantum information; Hilbert spaces; physical systems; unitary; collapse; Euler angles parametrization; Copenhagen interpretation; many- world; measure;

    Abstract : We focus on the Tensor Product Structure (TPS) of the Hilbert space and the fact that a choice in the TPS has an impact on the representation of the studied quantum system. We define the measurement problem in quantum mechanics and present some theories about quantum mechanics, each of them highlighting a different approach to quantum measurements. READ MORE

  3. 2. Discussion of Python Implementation Techniques for Discontinuous Galerkin Methods

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Ulf Vestberg; [2023]
    Keywords : Best approximation; Orthogonal polynomials; Legendre polynomials; Integration; Full tensor product; Sum-factorization; Dune; Mathematics and Statistics;

    Abstract : This paper discusses implementation techniques for integration methods within the Discontinuous Galerkin Methods. These methods are used to approximate solutions for differential equations. To do so, one must compute a polynomial, which is an approximation of the used function. READ MORE

  4. 3. A Hierarchical Tucker Solver for the Vlasov-Maxwell System

    University essay from Uppsala universitet/Institutionen för informationsteknologi

    Author : Oskar Tegby; [2023]
    Keywords : ;

    Abstract : The Vlasov-Maxwell equations is a common model to describe the behavior of a plasma, but come at the cost of their dimensionality since both spatial and veloocity data is stored in three dimensions. This causes a significant obstacle to be able solve them numerically since the size of the data is N^6, which yields a data size of 8. READ MORE

  5. 4. Designing Effective Derivative Line Filters: Utilizing convolution to extract extra information

    University essay from KTH/Matematik (Avd.)

    Author : Gustaf Lorentzon; [2023]
    Keywords : Computational Fluid Dynamics; Convolution Filters; Convolution Kernels; Derivatives; Extracting Extra Accuracy; Filtration; Post-processing; Smoothness-Increasing Accuracy-Conserving; Signal-processing; Visualization; Vorticity; Beräkningsbaserad Strömningsdynamik; Faltningsfilter; Faltningskärnor; Derivator; Extrahering av Extra Noggrannhet; Filtrering; Efterbehandling; Kontinuitetsökande; Noggrannhetsbevarande; Signalbehandling; Visualisering; Vorticitet;

    Abstract : The ability to generate accurate approximations of derivatives holds significant importance in numerous scientific fields, including chemistry, economics and fluid mechanics. This thesis is centred around extracting hidden information in data using Smoothness-Increasing Accuracy-Conserving (SIAC) filters. READ MORE

  6. 5. Tensor rank and support rank in the context of algebraic complexity theory

    University essay from KTH/Matematik (Avd.)

    Author : Pelle Andersson; [2023]
    Keywords : linear algebra; tensor product; tensor rank; matrix multiplication; complexity; linjär algebra; tensorprodukt; tensorrang; matrismultiplikation; komplexitet;

    Abstract : Starting with the work of Volker Strassen, algorithms for matrix multiplication have been developed which are time complexity-wise more efficient than the standard algorithm from the definition of multiplication. The general method of the developments has been viewing the bilinear mapping that matrix multiplication is as a three-dimensional tensor, where there is an exact correspondence between time complexity of the multiplication algorithm and tensor rank. READ MORE