On page 64 it is written that the max. abs. difference formula for decomposers:
max |A − LUP|
represents:
To clarify, the maximum absolute difference for decomposers is the largest absolute difference between a computed element and its expected result.
Consider replacing it with something like:
To clarify, the 'maximum absolute difference' for decomposers is defined as the largest absolute difference between the expected value of each element in the original matrix (A) and its corresponding computed value, represented in matrix form as LUP, after the LU decomposition process.
Similarly, for solvers change the clarification sentence from:
To clarify, the computed unknowns are used in the system of equations in matrix form, and then the largest absolute difference between the left- and right-hand sides is used.
to something like:
To clarify, the maximum absolute difference for solvers is calculated by comparing the computed unknowns (X) used in the system of equations, represented in matrix form as LUPX, with the right-hand side matrix (B). The metric measures the largest absolute difference between the elements of LUPX and the corresponding elements of B.
TODO: