#FoundationsOfAppliedMath - Twitter Hashtag

over 5 years ago

Automatic (a.k.a. algorithmic) differentiation is an amazing tool. It can differentiate efficiently and accurately almost any function you can compute, including those defined by complicated algorithms #FoundationsOfAppliedMath https://t.co/fkAu560yKb

tj_jarvis's tweet photo. Automatic (a.k.a. algorithmic) differentiation is an amazing tool. It can differentiate efficiently and accurately almost any function you can compute, including those defined by complicated algorithms #FoundationsOfAppliedMath https://t.co/fkAu560yKb https://t.co/nZUeOuc8KE

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Tyler Jarvis @tj_jarvis

over 5 years ago

@m_letitbe @robertkaplinsky "Things you will use" and "train to think critically..." are not mutually exclusive. So why not spend our time on the things that do both? #FoundationsOfAppliedMath

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Tyler Jarvis @tj_jarvis

over 5 years ago

Newton's method converges in very few steps but each step is an expensive O(n^3) operation. BFGS reduces the cost of each step to O(n^2). It takes more steps to converge but in high dimensions can be faster overall #FoundationsOfAppliedMath @TheSIAMNews https://t.co/kmtdVLEb6C

tj_jarvis's tweet photo. Newton's method converges in very few steps but each step is an expensive O(n^3) operation. BFGS reduces the cost of each step to O(n^2). It takes more steps to converge but in high dimensions can be faster overall #FoundationsOfAppliedMath @TheSIAMNews https://t.co/kmtdVLEb6C https://t.co/8i7g7IjTol

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Tyler Jarvis @tj_jarvis

over 5 years ago

The degree-d polynomial interpolating at Chebyshev points in [-1,1] can be computed using the FFT in O(d log d) time, and the error shrinks rapidly with d, if the function being approximated is relatively smooth #FoundationsOfAppliedMath https://t.co/kmtdVLEb6C

tj_jarvis's tweet photo. The degree-d polynomial interpolating at Chebyshev points in [-1,1] can be computed using the FFT in O(d log d) time, and the error shrinks rapidly with d, if the function being approximated is relatively smooth #FoundationsOfAppliedMath https://t.co/kmtdVLEb6C https://t.co/ZnrqIzrG6e

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Tyler Jarvis @tj_jarvis

over 5 years ago

Perron's theorem: A matrix A with all positive entries has a simple, real eigenvalue λ equal to the spectral radius r(A) and it has a positive eigenvector. All the eigenvalues lie in the ball B(ε,λ–ε) for small enough ε>0 #FoundationsOfAppliedMath

tj_jarvis's tweet photo. Perron's theorem: A matrix A with all positive entries has a simple, real eigenvalue λ equal to the spectral radius r(A) and it has a positive eigenvector. All the eigenvalues lie in the ball B(ε,λ–ε) for small enough ε>0 #FoundationsOfAppliedMath https://t.co/WSIdVWZv7u

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Tyler Jarvis @tj_jarvis

over 6 years ago

I am very flattered that @jamestanton likes these books by Emily Evans, @JeffHumpherys, and me. James is a genius teacher and inspires much of what I do on the classroom, in my writing, and beyond #FoundationsOfAppliedMath

James Tanton

@jamestanton

over 6 years ago

These volumes already are classics in my mind! Brilliant, beautiful, astoundingly comprehensive masterpieces. (You can make out the title details if you enlarge the photo.)

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