Essays about: "linjär algebra"

Showing result 1 - 5 of 14 essays containing the words linjär algebra.

  1. 1. Randomized Diagonal Estimation

    University essay from KTH/Matematik (Avd.)

    Author : Niclas Joshua Popp; [2023]
    Keywords : Diagonal estimation; randomized numerical linear algebra; low-rank approximation; matrix functions; Diagonalestimering; randomiserad numerisk linjär algebra; lågrankad approximation; matrisfunktioner;

    Abstract : Implicit diagonal estimation is a long-standing problem that is concerned with approximating the diagonal of a matrix that can only be accessed through matrix-vector products. It is of interest in various fields of application, such as network science, material science and machine learning. READ MORE

  3. 2. Building a Deep Neural Network From Scratch

    University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Author : Fredrik Sundström; Samppa Raittila; [2023]
    Keywords : ;

    Abstract : Machine learning is becoming increasingly common in our society and is predictedto have a major impact in the future. Therefore, it would be both interesting and valuable tohave a deep understanding of one of the most used algorithms in machine learning, deepneural network. READ MORE

  4. 3. 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

  5. 4. Perron-Frobenius' Theory and Applications

    University essay from Linköpings universitet/Algebra, geometri och diskret matematik; Linköpings universitet/Tekniska fakulteten

    Author : Karl Eriksson; [2023]
    Keywords : Positive matrices; nonnegative matrices; Perron-Frobenius; linear dynamical systems; Leslie matrices; Markov chain; Google s PageRank algorithm; Positiva matriser; icke-negativa matriser; Perron-Frobenius; linjära dynamiska system; Leslie matris; Markov-kedja; Google s PageRank algoritm;

    Abstract : This is a literature study, in linear algebra, about positive and nonnegative matrices and their special properties. We say that a matrix or a vector is positive/nonnegative if all of its entries are positive/nonnegative. First, we study some generalities and become acquainted with two types of nonnegative matrices; irreducible and reducible. READ MORE

  6. 5. Benchmarking linear-algebra algorithms on CPU- and FPGA-based platforms

    University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Author : Omar Askar Vergara; Karl Törnblom Bartholf; [2023]
    Keywords : FPGA; OpenCL; PolyBench; Cholesky; Durbin;

    Abstract : Moore’s law is the main driving factor behind the rapid evolution of computers that has been observed in the past 50 years. Though the law is soon ending due to heat- and sizing-related issues. One solution to continuing the evolution is utilizing alternative computer hardware, where parallel hardware is especially interesting. READ MORE