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> it's definitely NOT in departments of computer science. Instead look at selected programs in pure/applied math in some of the best research universities. Sli

> it's definitely NOT in departments of computer science. Instead look at selected programs in pure/applied math in some of the best research universities. Slight qualification: It's in pure/applied math in some of the best research universities, BUT, it needs a CS treatment, i.e., it needs to be utilized as numerical programming, not pen-and-paper math. I would also claim that the pure/applied math guys (MS, PhDs) don't have much edge here unless they shed their pen-and-paper habits and embrace computer-science. (likewise, CS MS,PhDs don't have an edge as long as they keep calling their discrete-algorithms class, free of numerical analysis and scientific computing, Algorithms! the exceptions are computer-graphics researchers, DSP, numerical-analysists etc). And those who are good at both pure/applied-math as well as programming/software-engineering, (cough humblebrag cough) boy...!

graycat 9y ago
Numerical analysis is an old field. Some of it was condition number of matrices and the resulting error analysis. Some of it was, say, double precision inner product accumulation and, for solving linear systems, iterative improvement. There was a lot more for solving ordinary (e.g., stiff) and partial differential equations. Courant was good at that. Too soon, e.g., trying to solve the Navier Stokes equations, numerical analysis gets quite deep into pure/applied math -- there's no royal road there through the CS departments and no royal road at all. E.g., a good prerequisite for work in numerical analysis is a high end course in linear algebra, e.g., matrix norms, Gershgorin approximations; not many people teach or take such a course. E.g., polynomial curve fitting can quickly lead people to solving a systems of statistics normal equations with the notoriously ill-conditioned Hilbert matrix. But, with some orthogonal polynomial approaches, can get around the numerical problems right away. I did that once for some profs at Georgetown U. I'd learned how to do that consulting in applied math and numerical analysis. For more, the days of ill-conditioned matrices led M. Newman to multiply the equations by large powers of 10 so that he had all whole numbers. Then for each prime number in a list of prime numbers, he solved the equations in the field of the integers modulo that prime. Right, for the multiplicative inverse, use the Euclidean greatest common divisor algorithm. Cute. Then use the Chinese remainder theorem to glue together the answers as quotients of multiple precision whole numbers. Ah, numerical analysis! Guys, that's not computer science, no matter how many nVidia GPUs they keep busy.

graycat 9y ago

Numerical analysis is an old field. Some of it was condition number of matrices and the resulting error analysis. Some of it was, say, double precision inner product accumulation and, for solving linear systems, iterative improvement. There was a lot more for solving ordinary (e.g., stiff) and partial differential equations. Courant was good at that. Too soon, e.g., trying to solve the Navier Stokes equations, numerical analysis gets quite deep into pure/applied math -- there's no royal road there through the CS departments and no royal road at all. E.g., a good prerequisite for work in numerical analysis is a high end course in linear algebra, e.g., matrix norms, Gershgorin approximations; not many people teach or take such a course. E.g., polynomial curve fitting can quickly lead people to solving a systems of statistics normal equations with the notoriously ill-conditioned Hilbert matrix. But, with some orthogonal polynomial approaches, can get around the numerical problems right away. I did that once for some profs at Georgetown U. I'd learned how to do that consulting in applied math and numerical analysis. For more, the days of ill-conditioned matrices led M. Newman to multiply the equations by large powers of 10 so that he had all whole numbers. Then for each prime number in a list of prime numbers, he solved the equations in the field of the integers modulo that prime. Right, for the multiplicative inverse, use the Euclidean greatest common divisor algorithm. Cute. Then use the Chinese remainder theorem to glue together the answers as quotients of multiple precision whole numbers. Ah, numerical analysis! Guys, that's not computer science, no matter how many nVidia GPUs they keep busy.