Week 3: Memory, floating point, LU decomposition

Stack, Heap, Allocations

• How programs get their memory ?

• Why are allocations slow ?

• Why stack is scarce ?

• Why don't we free memory in Julia ?

• Pluto notebook: pluto/julia, html, pdf,

Floating point representation

• Why is 0.1+0.2 = 0.30000000000000004 ?

• Why is 1.0 + 1.0e-17 = 1.0 ?

• How many numbers are there per unit interval ?

• Pluto notebook: pluto/julia, html, pdf,

LU Factorization, direct solvers

• Why shouldn't we write x=inv(A)*b when we want to solve $Ax=b$ ?

• How fast is the solution of a linear system of equations

• Pluto notebook: pluto/julia, html, pdf,

Finite Difference matrices from PDEs

• How do matrices from PDEs look ?

• Don't we waste memory when we store them ?

• Pluto notebook: pluto/julia, html, pdf,