This app uses high precision arithmetic in software to implement a QR factorization of a complex matrix.
The high precision arithmetic software library is from:
http://www.apfloat.org/apfloat_java/
The computation of the Householder vector follows the definition given in:
http://arith.cs.ucla.edu/publications/House-Asil06.pdf
While this does give the correct answer, compared to a simple Java version, I don't consider it particularly
useful because of the time consumed in the software implementation of arithmetic operations. For example,
running on a 2019 variety mobile phone the execution times for a 192x120 matrix are:
extended precision: 60 seconds
Java double precision: 100 milliseconds
Arm64 assembly: 3.5 milliseconds
If the matrices were very large, where 64 bit floating point was inadequate, a parallel implementation
would be necessary.
These results are in contrast to a backsolve operation where complex matrices as small as 64x64 start to
benefit and are required at size 128x128.