CAAM 551: Advanced Numerical Linear Algebra

Notes on Dense Numerical Linear Algebra

  • set1.pdf Intro material, Polynomial interpolation and best fit, Orthogonal and unitary transformations
  • set2.pdf Matrix and Vector Norms
  • set3.pdf The SVD, Four fundamental spaces, Best rank k approximation
  • set4.pdf Projectors, Decompositions of C^n, Orthogonal Projections, Fundamental projections from SVD
  • set5.pdf Projections, Least Squares via SVD, LS via QR Factorization
  • set6.pdf Least Squares via Householder QR, LS via Normal Equations
  • set7.pdf Condition Numbers, Perturbations, Sensitivity of Linear systems and Least Squares
  • set8.pdf Finite Precision Arith., Backward Error Analysis: Householder method and triangular solves
  • set9.pdf LU Factorization, Ax = b, Backward Error Analysis, Condition Estimation
  • set10.pdf Eigenspaces: Schur Decompositon, Spectral Theory, Sylvesters Equation, Cayley Hamilton
  • set11.pdf Ax = x lambda: Simple eigenvalue methods, Power, Inverse Power, Inverse Iteration
  • SymmIndefFac.pdf The Symmetric Indefinite Factorization
  • LectureNotes08 551 Course Lecture Notes 2008