CS070/CS170, Spring 2013
Numerical and Computational Tools for Applied Science

This page will be updated frequently with current and upcoming topics.


March 26Introduction, class objectives and policies
HW 0
March 28Hands-on Introduction to Matlab HW 0
April 2
HW 1
April 4
April 9
HW 2HW 1
April 11
April 16Orthogonality
HW 2
April 18SVD
April 23Eigenvalue problem continued; PCA HW 3
April 25
April 30
Project ProposalHW 3
May 2
May 7No class
Project Proposal
May 9No class
May 14
May 16
May 21Project presentations:
  • Haddadan Shahrzad, Panotopoulou Athina, Sarroff Andrew
  • Kang Yaozhong, Li Tian, Liu Zheyu, Xing Yue
  • Zhang Rongxiao, An Chao, Feng Wenyuan, Li Yanan
  • Li Xin, Tan Jie, Zhou Jianfu
May 23Project presentations:
  • Hou Ruixuan, Li Jing
  • Jenkins Ira, Pierson Timothy
  • Cheng Yuting, Su Chengwei, Wang Xin, Wang Zhenghui
  • Miao Yusheng, Wang Qiuhan
May 28Project presentations:
  • Hansen Anders, Lachance Katherine
  • Madsen Thomas, Zupan Nejc
  • Chen Fanglin, Wang Rui
  • Mao Weijia, Xu Ye
May 29Final Project due
Final Project


  • Matlab, part I:
    basic arithmetic; vectors and matrices; matrix arithmetic; control structures; input/output; scripts and functions.

  • Linear Algebra, solving Ax=b:
    row and column picture; Gaussian elimination; matrix inverse; Gauss-Jordan; LU factorization and its applications; vector spaces; geometric interpretations of nullspace, rowspace, columnspace and left nullspace of a matrix; algorithms to compute the nullspace, rowspace, columnspace and left nullspace of a matrix.

  • Matlab, part II:
    data structures; 1-D plotting; 2-D images; 3-D surfaces; GUI programming.

  • Least-squares estimation:
    applications: linear and nonlinear regression, data fitting; the calculus view: system of normal equations; the linear algebra view: geometric interpretation of least-squares fitting via projection onto the columnspace.

  • Singular Value Decomposition:
    orthogonal bases and matrices; geometric interpretation of SVD; applications: dimensionality reduction, rank computation; least squares-fitting via SVD: the pseudoinverse.

  • Eigenvectors and eigenvalues:
    discussion of special cases: projection matrix, permutation matrix, triangular matrix; characteristic equation; remarks on iterative methods for eigendecomposition; application: solving recursive matrix equations; application: Principal Component Analysis; PCA via SVD; eigenfaces for face recognition.

  • One dimensional optimization:
    golden section search; Newton's method.

  • Multidimensional unconstrained optimization:
    steepest descent, discussion of methods for line search; Newton's method; conjugate gradient (geometric interpretation, derivation for quadratic function, generalization to arbitrary function).

  • Constrained optimization:
    method of Lagrange multipliers.

  • Linear programming:
    simplex algorithm.