Numerical analysis NUAN

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Creating, analysing, implementing, testing and improving algorithms for numerically solving mathematical problems.

SFIA 9 is in development

SFIA 9 beta due in early July 2024
SFIA 9 planned for publication October 2024

Guidance notes

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Numerical analysis is the area of mathematics and computer science that creates, analyses, and implements algorithms for numerically solving mathematical problems. Numerical analysis is required for applications including, but not limited to:

simulations of physical systems
machine learning
data analytics

Numerical analysis is concerned with:

floating-point arithmetic and the resulting accumulation of rounding errors (integer arithmetic which has different considerations)
consideration of the numerical stability, condition numbers, accuracy, computational complexity and usability of algorithms that solve mathematical problems.

Understanding the responsibility levels of this skill

Where lower levels are not defined...

Specific tasks and responsibilities are not defined because the skill requires a higher level of autonomy, influence, and complexity in decision-making than is typically expected at these levels. You can use the essence statements to understand the generic responsibilities associated with these levels.

Where higher levels are not defined...

Responsibilities and accountabilities are not defined because these higher levels involve strategic leadership and broader organisational influence that goes beyond the scope of this specific skill. See the essence statements.

Developing skills and demonstrating responsibilities related to this skill

The defined levels show the incremental progression in skills and reponsibilities.

Where lower levels are not defined...

You can develop your knowledge and support others who do have responsibility in this area by:

Learning key concepts and principles related to this skill and its impact on your role
Performing related skills (see the related SFIA skills)
Supporting others with tasks (generic examples are provided by the essence statements for each level)

Where higher levels are not defined...

You can progress by developing related skills which are better suited to higher levels of organisational leadership.

Levels

Defined at these levels:

Click to learn why SFIA skills are not defined at all 7 levels.

Show/hide extra descriptions and levels.

Level 1

Level 1 - Follow: Essence of the level: Performs routine tasks under close supervision, follows instructions, and requires guidance to complete their work. Learns and applies basic skills and knowledge.

Level 2

Level 2 - Assist: Essence of the level: Provides assistance to others, works under routine supervision, and uses their discretion to address routine problems. Actively learns through training and on-the-job experiences.

Level 3

Level 3 - Apply: Essence of the level: Performs varied tasks, sometimes complex and non-routine, using standard methods and procedures. Works under general direction, exercises discretion, and manages own work within deadlines. Proactively enhances skills and impact in the workplace.

Numerical analysis: Level 4

Level 4 - Enable: Essence of the level: Performs diverse complex activities, supports and supervises others, works autonomously under general direction, and contributes expertise to deliver team objectives.

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Creates moderately complex algorithms using a range of mathematical techniques and with sensitivity to the limitations of the techniques.

Uses sophisticated scientific computing and visualisation environments.

Assesses the stability, accuracy and efficiency of algorithms and makes or recommends improvements to them.

Iterates and improves models using feedback from experts as appropriate.

Numerical analysis: Level 5

Level 5 - Ensure, advise: Essence of the level: Provides authoritative guidance in their field and works under broad direction. Accountable for achieving workgroup objectives and managing work from analysis to execution and evaluation.

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Creates, tests and improves complex algorithms that numerically solve real-world problems.

Develops mathematical and computational techniques to assist with numerical analysis.

Communicates limitations such as uncertainty and systematic errors.

Reviews algorithms for their conformance to design and performance standards.

Numerical analysis: Level 6

Level 6 - Initiate, influence: Essence of the level: Has significant organisational influence, makes high-level decisions, shapes policies, demonstrates leadership, fosters organizational collaboration, and accepts accountability in key areas.

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Initiates the creation, testing, improvement and application of numerical algorithms that solve real-world mathematical problems.

Sets standards and strategies for the application of numerical analysis.

Leads the implementation of numerical analyses capabilities to ensure appropriate, consistent and effective usage across the organisation.

Numerical analysis: Level 7

Level 7 - Set strategy, inspire, mobilise: Essence of the level: Operates at the highest organisational level, determines overall organisational vision and strategy, and assumes accountability for overall success.

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Directs the creation and review of a cross-functional, enterprise-wide approach and culture for numerical analysis.

Leads the development of the organisation’s numerical analysis capabilities and champions its use in solving real-world problems.