mathematics

William B. Gragg

William B. Gragg is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand William B. Gragg rather than just read about it. In short: William B. Gragg (2 November 1936 – 25 December 2016) ended his career as an emeritus professor in the Department of Applied Mathematics at the Naval Postgraduate School.

Key takeaways

William B. Gragg belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect William B. Gragg to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of William B. Gragg from memory before moving on to harder problems.

Reference excerpt

William B. Gragg (2 November 1936 – 25 December 2016) ended his career as an emeritus professor in the Department of Applied Mathematics at the Naval Postgraduate School. He has made fundamental contributions in numerical analysis, particularly the areas of numerical linear algebra and numerical methods for ordinary differential equations. He received his PhD at UCLA in 1964 under the direction of Peter Henrici. His dissertation work resulted in the Gragg Extrapolation method for the numerical solution of ordinary differential equations (sometimes also called the Bulirsch–Stoer algorithm). Gragg is also well known for his work on the QR algorithm for unitary Hessenberg matrices, on updating the QR factorization, superfast solution of Toeplitz systems, parallel algorithms for solving eigenvalue problems, as well as his exposition on the Pade table and its relation to a large number of algorithms in numerical analysis.

References

External links William B. Gragg at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with William B. Gragg

Start with the simplest possible case. Write down what William B. Gragg claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to William B. Gragg before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about William B. Gragg ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of William B. Gragg

In research: William B. Gragg appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses William B. Gragg in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: William B. Gragg is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1936 births, 2016 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for William B. Gragg outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study William B. Gragg in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what William B. Gragg means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain William B. Gragg out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is William B. Gragg in simple terms?

William B. Gragg (2 November 1936 – 25 December 2016) ended his career as an emeritus professor in the Department of Applied Mathematics at the Naval Postgraduate School.

Why does William B. Gragg matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study William B. Gragg?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on William B. Gragg.