Deniz Bilman
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  • Teaching
    • Numerical Linear Algebra
      • Lecture 1
      • Lecture 2
      • Lecture 3
      • Lecture 4
      • Lecture 4 (Applications)
      • Lecture 5
      • Lecture 6
      • Lecture 7
      • Lecture 8
      • Lecture 10
      • Lecture 11
      • Lecture 12
      • Lecture 13
      • Lectures 14-15
      • Lecture 16
      • Lecture 17
      • Lecture 20
      • Lecture 21
      • Lecture 22
      • Lecture 23
      • Lecture 24
      • Lecture 25
      • Lecture 26
      • Lecture 27
      • Lecture 28
    • Ordinary Differential Equations
      • Lecture 1
      • Lecture 2
      • Lecture 3
      • Lecture 4
      • Lecture 5
      • Lecture 6
      • Lecture 7
      • Lecture 8
      • Lecture 9
      • Lecture 10
      • Lecture 11
      • Lecture 12
      • Lecture 13
      • Lecture 14
      • Lecture 15
      • Lecture 16
      • Lecture 17
      • Lecture 18
      • Lecture 19
      • Lecture 20
      • Lecture 21
      • Appendix 1
      • Appendix 2
    • Partial Differential Equations
      • Lecture 1
      • Lecture 2
      • Lecture 3
      • Lecture 4
      • Lecture 5
      • Lecture 6
      • Lecture 7
      • Lecture 8
      • Lecture 9
      • Lecture 10
      • Lecture 11
      • Lecture 12
      • Lecture 13
      • Lecture 14
      • Lecture 15
      • Lecture 16
      • Lecture 17
      • Lecture 18
      • Lecture 19
      • Appendix 1
  • Blog
    • Special session at the IMACS Conference 2025 in Athens, GA
    • New paper!
    • RogueWaveInfiniteNLS.jl software package for Julia
    • Special session at the AMS Joint Math Meeting 2025 in Seattle, WA
  • Publications
    • General rogue waves of infinite order: exact properties, asymptotic behavior, and effective numerical computation
    • Extreme superposition: high-order fundamental rogue waves in the far-field regime
    • RogueWaveInfiniteNLS.jl
    • Computation of large-genus solutions of the Korteweg-de Vries equation
    • Broader universality of rogue waves of infinite order
    • Far-field asymptotics for multiple-pole solitons in the large-order limit
    • On numerical inverse scattering for the Korteweg-de Vries equation with discontinuous step-like data
    • Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy
    • Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
    • Benchmarking numerical methods for lattice equations with the Toda lattice
    • A robust inverse scattering transform for the focusing nonlinear Schrödinger equation
    • Discrete integrable systems, Darboux transformations, and Yang–Baxter maps
    • Numerical inverse scattering for the Toda lattice
    • On the evolution of scattering data under perturbations of the Toda lattice
  • In preparation
    • General rogue waves of infinite order: double-scaling asymptotics
    • Solitons of fractional order: interpolating between coherent structures
    • Infinite-order solutions of the modified Korteweg-de Vries equation
    • Asymptotic behavior of large-order soliton solutions of the modified Korteweg-de Vries equation
    • Far-field symptotics of large-order breathers for the sine-Gordon equation
    • Long-time development of initial data with spectral pole singularities
    • Long-time asymptotics for the Korteweg-de Vries equation
    • Contact
Teaching
Numerical Linear Algebra
Lecture 5

More on the SVD

Jan 29, 2025 · 1 min read
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Last updated on Jan 29, 2025
Deniz Bilman
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Deniz Bilman
Assistant Professor
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