Course title
6M0048001
Mathematics for Numerical Computations

 ozaki katsuhisa Click to show questionnaire result at 2019
Course content
Numerical Computation is performed very fast on today's architectures. However, since floating-point number has finite precision, rounding error may occur in each operation. If rounding errors accumulate, the computed result may be inaccurate. Verified Numerical Computations (VNC) can check stability of the numerical results. In this class we learn elemental topics about VNC.
Purpose of class
First, students learn definition of floating-point numbers and floating-point arithmetic. Next topic is error analysis. The purpose is to understand rounding errors for floating-point arithmetic.
Goals and objectives
  1. understanding floating-point numbers and floating-point arithmetic
  2. understanding rounding errors in floating-point arithmetic
  3. understanding how to analyze an upper bound of rounding errors
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． floating-point numbers review of binary numbers 190minutes
2． floating-point arithmetic review of floating-point numbers 190minutes
3． a priori error analysis: summation and dot product review of floating-point arithmetic 190minutes
4． a priori error analysis: Horner's method review of error-analysis 190minutes
5． a priori error analysis: LU decomposition review of LU decomopsition 190minutes
6． linear systems review of matrix and vector norms 190minutes
7． eigen value problems review of eigen value problems 190minutes
8． total review total review 190minutes
9． interval arithmetic review of intervals 190minutes
10． interval arithmetic for matrix multiplication review of interval arithmetic 190minutes
11． VNC: matrix non-singularity review of interval matrix multiplication 190minutes
12． VNC: linear systems how to use MATLAB 190minutes
13． VNC: matrix determinant review of matrix determinant 190minutes
14． examination and its remark total review 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 exam Total.
1. 40% 40%
2. 30% 30%
3. 30% 30%
Total. 100% -
Evaluation method and criteria
Score of test.
Textbooks and reference materials
Nothing
Prerequisites
Review of numerical analysis.
Office hours and How to contact professors for questions
  • Lunch Time on Monday
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates a basic self-management skills
Active-learning course
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicatable
N/A N/A
Education related SDGs:the Sustainable Development Goals
    Last modified : Sat Mar 21 13:13:40 JST 2020