CmpE 482 Sp.Tp. Numerical Linear Algebra and Its Applications 2014 Spring

I Fundamentals

• Matrix-Vector Multiplication

• Orthogonal Vectors and Matrices

• Vector and Matrix Norms

• Singular Value Decomposition

• Application: Document Retrieval, Latent Semantic indexing, Procrustes analysis

II QR Factorization

• Projectors

• Gram-Schmidt Orthogonalization, QR Factorization

• MATLAB

• Householder Triangularization

• Least Square Problems

• Application: Polynomial and Basis Regression

III Conditioning and Stability

• Conditioning and Condition numbers

• Floating Point Arithmetic

• Stability

V Eigenvalues

• Eigenvalue Problems

• Overview of Eigenvalue Algorithms

• Reduction to Hessenberg or Tridiagonal form

• Rayleight Quotient, Inverse Iteration

• QR algorithm without/with shifts

• Computing the SVD

• Application: Spectral Clustering, Image segmentation