Professor Eric Polizzi

Class Hours: Tue-Thu 1:00pm-2:15pm LGRT 204

Office Hour: Wed 1:00-2:00pm in Marcus 201C
Syllabus
Introduction

 Schedule
 H O M E W O R K

HW1 [HW1]
HW2 [HW2]
HW3 [HW3]
HW4 [HW4]
HW5 [HW5]

 C O M P L E M E N T   and   R E F E R E N C E S

Code Examples - Fortran [zip]
Linux [Quick][Tutorial]
Fortran references[Quick] [Fortran vs C]
BLAS routines [Quick reference]
Gnuplot[Tutorial]
Templates Algo. [Templates]
List of free linear algebra package [Link]
IDRIS-MPI [Class Notes]
IDRIS-OpenMP [Class Notes] Code Examples - MPI [zip] and OpenMP [zip]

 C O N T E N T S

I- Introduction to Scientific Computing
• 1- Modeling process- 1D case study examples:
a- Electrostatics -DRAFT-
b- Thermal Conduction -DRAFT-
c- Confinement -DRAFT-
• 2- Higher Dimensions- 2D example -DRAFT-
• 3- Computing Framework Summary -DRAFT-
a- numerical error; b- matrix computations
II- Basic numerical techniques of linear algebra and their applications
• 1- Background -DRAFT-
a- vector; b-matrix; c-Subspace; d-non-singularity and inverses; e-types of square matrices;
• 2- Norms -DRAFT-
a- vector norms; b- matrix norms; condition number;
• 3- Solving Linear systems
a- introduction; -DRAFT-
b- Gaussian elimination and LU factorization -DRAFT-
c- Failure of LU, d- Complement, e- Cholesky Factorization -DRAFT-
• 4- Computational Primitives and Practices
a- BLAS, b- LAPACK, c- Programming practices -DRAFT-
• 5- Linear Least-Squares Problems
a- introduction, b- solving the linear least-squares, c- QR factorization, d- Singular Value Decomposition, e- discussions -DRAFT-
• 6- Eigenvalue Problems
a- introduction, b- Schur form and Jordan form, c- Eigendecomposition, d- computing the eigenvalue problem, e- QR algorithm, f- complements -DRAFT-
III- Data formats and Practices
DRAFT
• 1- Data Structures
a- dense format, b-banded format, c- sparse format
• 2- Sparse Matrix Computations: Practices
a- Introduction, b- Solving linear systems in Computational Sciences, c- Sparse solvers
IV- Solving large sparse linear systems and eigenvalue problems
• 1- Introduction to iterative methods for linear systems
a- basics, b- Family of standard iterative methods, c- introduction to Preconditioning DRAFT
• 2- Projection Methods
a- basics, b- steepest descent, c- conjugate gradient DRAFT
• 3- Krylov Subspace Methods a- Overview, b- Arnoldi algorithm, c- GMRES, d- the symmetric case, e- Preconditioning and Practices DRAFT
• 4- Large sparse eigenvalue problems
a- Intro, b- Arnoldi and Lanczos algorithms, c- Rayleigh-Ritz and Subspace Iterations draft
feast
V- Introduction to Parallel Programming
VI- Numerical parallel algorithms