- Person
- Harry Markowitz
- Lived
- 1927–2023
- Field
- Financial economics
- From
- American
The story
In the 1950s Harry Markowitz worked at the RAND Corporation with Alan Manne, Tibor Fabian, Thomas Marschak, Alan Rowe and others on large models of the industrial capabilities of whole industries and groups of industries. Solving these models meant handling huge tables of numbers, called matrices, and they strained the computers of the day.
Markowitz noticed that most of the coefficients in their matrices were zero; the non-zero entries were sparse. He also observed that when the equations were solved by Gaussian elimination, the standard step-by-step method, the matrices produced along the way would remain sparse if the pivot elements, the entries used to eliminate the others, were chosen with care. That meant a computer could store and work with only the non-zero entries, saving both memory and time. The term "sparse matrix" itself was possibly coined by Markowitz.
William Orchard-Hays programmed the first sparse matrix code. In 1957 Markowitz published "The Elimination Form of the Inverse and Its Application to Linear Programming" in the journal Management Science, setting out the approach for linear programming, the mathematics of making the best use of limited resources. Having started the field, he moved on to other problems.
Others took up the work. In Markowitz's words, considerable work has since been done on methods of selecting pivots and of storing the non-zero elements. Sparse matrix techniques became standard in large linear programming codes, and they are now widely used to solve very large systems of equations whose coefficients are mostly zero. Such systems arise throughout science and engineering, for example when partial differential equations are solved by the finite element method.
The work was one of three areas cited when Markowitz received the 1989 John von Neumann Theory Prize from the Operations Research Society of America and the Institute of Management Sciences, alongside portfolio theory and the SIMSCRIPT simulation language.
Why it matters
Sparse matrix techniques let computers solve very large systems of equations efficiently, making big planning, optimisation and engineering problems practical.
About Harry Markowitz
Chicago grocer’s son whose 1952 paper ‘Portfolio Selection’ founded modern portfolio theory, the mathematics of diversification behind how the world invests. Nobel 1990.
More about Harry Markowitz
- Harry Markowitz developed buddy memory allocationHarry Markowitz developed the buddy memory allocation method, included in the first version of his SIMSCRIPT language, a technique for managing computer memory.
- Harry Markowitz showed how to compute efficient portfoliosHarry Markowitz developed the critical line algorithm, published in 1956, to compute the efficient frontier, the set of portfolios giving the best return for each level of risk.
- Harry Markowitz created the SIMSCRIPT simulation languageIn the early 1960s Harry Markowitz returned to RAND to develop SIMSCRIPT, a programming language that made computer simulations much faster to build.
- Harry Markowitz wrote the book on efficient diversificationHarry Markowitz’s 1959 book Portfolio Selection: Efficient Diversification of Investments, written at Yale’s Cowles Foundation, set out his theory in full.
- Harry Markowitz turned diversification into a scienceIn his 1952 paper “Portfolio Selection”, Harry Markowitz showed mathematically how investors can reduce risk through diversification, founding modern portfolio theory.
Sources
- Harry M. Markowitz: Biographical NobelPrize.org
- Harry Markowitz Wikipedia
- Sparse matrix Wikipedia
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