[HN Gopher] Efficient simulation through linear algebra
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       Efficient simulation through linear algebra
        
       Author : martinhath
       Score  : 88 points
       Date   : 2022-08-13 16:28 UTC (1 days ago)
        
 (HTM) web link (mht.wtf)
 (TXT) w3m dump (mht.wtf)
        
       | tehsauce wrote:
       | Really nice article! I recently had a fun discovery that it's
       | possible to implement a reasonably efficient GPU sprite renderer
       | using linear algebra with sparse arrays + jit in jax. The quick
       | writeup - https://pwhiddy.github.io/more-writing/2022/07/20/Jax-
       | Sprite...
        
       | cyber_kinetist wrote:
       | Ah, the good ol' Sherman-Morrison formula.
       | (https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formu...)
       | Really useful to know sometimes.
       | 
       | A more general formula is known as the Woodbury matrix identity
       | (https://en.wikipedia.org/wiki/Woodbury_matrix_identity), which
       | comes up quite a lot in numerical algorithms.
        
         | onos wrote:
         | I've never seen these applied to a problem other than when one
         | wants to increase the dimension of the matrix by one or vice
         | versa... very eye opening. Will look for applications in my own
         | work now.
         | 
         | Also appreciated the derivation of sorts of the formula,
         | starting with the case where the main matrix is the identity.
        
       | jethkl wrote:
       | +1 to the article. Good job.
       | 
       | One suggestion: when experimenting, monitor numerical precision.
       | This is important if matrices are poorly conditioned or if the
       | inverse is updated over many iterations.
       | 
       | Also possibly of interest are Suitesparse and a Python-based
       | guide that uses it [1,2].
       | 
       | [1] https://people.engr.tamu.edu/davis/suitesparse.html
       | 
       | [2] https://cvxopt.org/userguide/spsolvers.html#
        
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       (page generated 2022-08-14 23:01 UTC)