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1. 1. Numerical methods for Sylvester-type matrix equations and nonlinear eigenvalue problems

   Författare :Emil Ringh; Elias Jarlebring; Johan Karlsson; Per Enqvist; Daniel Kressner; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Matrix equations; Lyapunov equation; Sylvester equation; nonlinear eigenvalue problems; two-parameter eigenvalue problems; Krylov methods; iterative methods; preconditioning; projection methods; Matrisekvationer; Lyapunovekvationen; Sylvesterekvationen; ickelinjära egenvärdesproblem; två-parameters egenvärdesproblem; Krylovmetoder; iterativa metoder; förkonditionering; projektionsmetoder; Tillämpad matematik och beräkningsmatematik; Applied and Computational Mathematics; Optimization and Systems Theory; Optimeringslära och systemteori; Numerical Analysis; Numerisk analys;

   Sammanfattning : Linear matrix equations and nonlinear eigenvalue problems (NEP) appear in a wide variety of applications in science and engineering. Important special cases of the former are the Lyapunov equation, the Sylvester equation, and their respective generalizations. These appear, e.g. LÄS MER

3. 2. Improving the efficiency of eigenvector-related computations

   Författare :Angelika Beatrix Schwarz; Lars Karlsson; Bo Kågström; Carl Christian Kjelgaard Mikkelsen; Miroslav Tůma; Umeå universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; high-performance computing; standard non-symmetric eigenvalue problem; triangular Sylvester equation; tiled algorithms; task parallelism;

   Sammanfattning : An effective strategy in dense linear algebra is the design of algorithms as tiled algorithms. Tiled algorithms that express the bulk of the computation as matrix-matrix operations (level-3 BLAS) have proven successful in achieving high performance on cache-based architectures. LÄS MER

4. 3. Algorithms and Library Software for Periodic and Parallel Eigenvalue Reordering and Sylvester-Type Matrix Equations with Condition Estimation

   Författare :Robert Granat; Bo Kågström; Isak Jonsson; Volker Mehrmann; Umeå universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; periodic eigenvalue problems; product eigenvalue problems; periodic Schur form; periodic eigenvalue reordering; periodic eigenspaces; parallel algorithms; Sylvester-type matrix equations; parallel eigenvalue reordering; condition estimation; Computer science; Datavetenskap;

   Sammanfattning : This Thesis contains contributions in two different but closely related subfields of Scientific and Parallel Computing which arise in the context of various eigenvalue problems: periodic and parallel eigenvalue reordering and parallel algorithms for Sylvestertype matrix equations with applications in condition estimation.Many real world phenomena behave periodically, e. LÄS MER

5. 4. Krylov methods for nonlinear eigenvalue problems and matrix equations

   Författare :Giampaolo Mele; Elias Jarlebring; Raf Vandebril; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Numerical Analysis; Numerisk analys;

   Sammanfattning : Nonlinear eigenvalue problems (NEPs) arise in many fields of science and engineering. Such problems are often defined by large matrices, which have specific structures, such as being sparse, low-rank, etc. Like the linear eigenvalue problem, the eigenvector appears in a linear form, whereas the eigenvalue appears in a nonlinear form. LÄS MER

7. 5. Singular Value Computations for Toeplitz Matrices and Subspace Tracking

   Författare :Eva Lundström; Henk van der Vorst; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY;

   Sammanfattning : This thesis addresses the problem of computing the largest singular values and corresponding singular vectors of a Toeplitz matrix. These are often requested in signal processing and system identification to extract the signal from the noise. LÄS MER