mathematics

Vera Kublanovskaya

Vera Kublanovskaya 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 Vera Kublanovskaya rather than just read about it. In short: Vera Nikolaevna Kublanovskaya (née Totubalina; November 21, 1920 – February 21, 2012 ) was a Russian mathematician noted for her work on developing computational methods for solving spectral problems of algebra. She proposed the QR algorithm for computing eigenvalues and eigenvectors in 1961, which has been named as one of the ten most important algorithms of the twentieth century.

Key takeaways

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

Reference excerpt

Vera Nikolaevna Kublanovskaya (née Totubalina; November 21, 1920 – February 21, 2012 ) was a Russian mathematician noted for her work on developing computational methods for solving spectral problems of algebra. She proposed the QR algorithm for computing eigenvalues and eigenvectors in 1961, which has been named as one of the ten most important algorithms of the twentieth century. This algorithm was proposed independently by the English computer scientist John G.F. Francis in 1961.

Early life Kublanovskaya was born in November 1920 in Krokhona, a village near Belozersk in Vologda Oblast, Russian Soviet Federative Socialist Republic. She was born in a farming and fishing family as one of nine siblings. She died at the age of 91 years old in February 2012.

Education Kublanovskaya started her tertiary education in 1939 at the Gertzen Pedagogical Institute in Leningrad. There, she was encouraged to pursue a career in mathematics. She moved on to study mathematics at Leningrad State University in 1945 and graduated in 1948. Following her graduation, she joined the Leningrad Branch of the Steklov Mathematical Institute of the USSR Academy of Sciences. She remained there for 64 years of her life. In 1955, she got her first doctorate degree on the application of analytic continuation to numeric methods. In 1972 she obtained a secondary doctorate on the use of orthogonal transformations to solve algebraic problems. In October 1985, she was awarded an honorary doctorate at Umeå University, Sweden, with which she has collaborated.

Scientific works During her first PhD, she joined Leonid Kantorovich's group that was working on developing a universal computer language in the USSR. Her task was to select and classify matrix operations that are useful in numerical linear algebra.

Publications On some algorithms for the solution of the complete eigenvalue problem On a method of solving the complete eigenvalue problem for a degenerate matrix Methods and algorithms of solving spectral problems for polynomial and rational matrices To solving problems of algebra for two-parameter matrices. V To solving problems of algebra for two-parameter matrices. IX

Notes

References Dongarra, Jack J.; Sullivan, Francis (2000), "Guest editors' introduction: The top 10 algorithms", Computing in Science & Engineering, 2 (1): 22–23, Bibcode:2000CSE.....2a..22D, doi:10.1109/MCISE.2000.814652, ISSN 1521-9615. Golub, Gene H.; Uhlig, Frank (2009), "The QR algorithm: 50 years later – its genesis by John Francis and Vera Kublanovskaya, and subsequent developments", IMA Journal of Numerical Analysis, 29 (3): 467–485, doi:10.1093/imanum/drp012, ISSN 0272-4979. Kon'kova, Ya.; Simonova, V.N.; Khazanov, V.B. (2000), "Vera Nikolaevna Kublanovskaya. Short Biography", Journal of Mathematical Sciences, 114 (6): 1755–56, doi:10.1023/A:1022491200674, S2CID 118551402.

External links MacTutor History of Mathematics biography

Worked examples

Example 1 — a first encounter with Vera Kublanovskaya

Start with the simplest possible case. Write down what Vera Kublanovskaya 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 Vera Kublanovskaya 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 Vera Kublanovskaya 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 Vera Kublanovskaya

In research: Vera Kublanovskaya 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 Vera Kublanovskaya 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: Vera Kublanovskaya is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1920 births, 2012 deaths, 20th-century Russian women scientists, so understanding it makes those chapters shorter.
In everyday life: Look for Vera Kublanovskaya 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 Vera Kublanovskaya in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Vera Kublanovskaya 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.
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Frequently asked questions

What is Vera Kublanovskaya in simple terms?

Why does Vera Kublanovskaya 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 Vera Kublanovskaya?

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 Vera Kublanovskaya.