In numerical computations, floating-point numbers and their operations, as defined by the IEEE 754 standard, are commonly
used. Since this system is widely employed in various simulations, it is essential to understand its principles correctly.
This lecture provides an overview of the system, covering the definitions and mathematical properties of floating-point numbers
and operations, as well as conducting an analysis of rounding errors.
The aim is to gain a deeper understanding of the computations handled in C language, MATLAB, and other environments. This
course covers binary floating-point numbers and issues related to rounding errors, enabling students to perform numerical
computations with a correct understanding of the system. Additionally, students will learn to conduct rounding error (absolute
error) analysis in simple linear computations.
- Be able to understand binary floating-point numbers as defined by the IEEE 754 standard.
- Be able to understand the properties of floating-point operations.
- Be able to perform rounding error analysis.
| report | Final report | Total. | |
|---|---|---|---|
| 1. | 10% | 20% | 30% |
| 2. | 10% | 20% | 30% |
| 3. | 10% | 30% | 40% |
| Total. | 30% | 70% | - |
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1． | Examples of numerical errors and the definition of floating-point numbers. | Review of numerical computations in C language and MATLAB | 180minutes |
| 2． | Definition of floating-point arithmetic. | Review of the definition of floating-point numbers | 180minutes |
| 3． | Mathematical properties of floating-point numbers and floating-point arithmetic. | Examples of errors and a review of the definition of floating-point operations | 180minutes |
| 4． | Models for rounding error analysis | Review of the definition of floating-point numbers | 180minutes |
| 5． | Rounding error analysis for summation | Review of models for rounding error analysis | 180minutes |
| 6． | Rounding error analysis for inner products | Review of rounding error analysis for summation | 180minutes |
| 7． | Final assignment and its review | Comprehensive review of all previous topics | 180minutes |
| 8． | For a one-credit course, lectures are held up to the seventh session | 0minutes | |
| 9． | For a one-credit course, lectures are held up to the seventh session | 0minutes | |
| 10． | For a one-credit course, lectures are held up to the seventh session | 0minutes | |
| 11． | For a one-credit course, lectures are held up to the seventh session | 0minutes | |
| 12． | For a one-credit course, lectures are held up to the seventh session | 0minutes | |
| 13． | For a one-credit course, lectures are held up to the seventh session | 0minutes | |
| 14． | For a one-credit course, lectures are held up to the seventh session | 0minutes | |
| Total. | - | - | 1260minutes |
Evaluation will be based on short reports for each lecture and a final report at the end of the term. To pass, students must
demonstrate an understanding of the fundamentals of the floating-point system and be able to perform rounding error analysis
independently.
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class |
- Course that cultivates a basic self-management skills
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
- 4.QUALITY EDUCATION
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Mon Feb 17 04:06:37 JST 2025