Lanczos and Einstein’s correspondence

Lanczos once wrote to Einstein about his work on iterative methods,

“The reason I am interested very much in dealing with methods of approximation is not the practical applicability of the solution but rather the fact that a very ‘economical’ solution is possible only if it is very ‘adequate’ too.  To get a solution in a few steps means nearly always that one has found a method which is consistent with the intrinsic nature of the problem.”

Einstein replied,

“Your remark concerning the significance of the adapted approximation methods is very enlightening, and I am convinced that it represents not merely a practical method but also is a promising mathematical viewpoint.”

[Via C. Brezinski , L. Wuytack, “Numerical Analysis in the 20th Century,” the Introduction to the volume “Numerical Analysis: Historical Developments in the 20th century” (eds. Brezinski and Wuytack, North-Holland, 2001)]

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