  Scientific computations or measurements may result in huge volumes of data.
Often these can be thought of representing a real-valued function on a
high-dimensional domain, and can be conceptually arranged in the format of a
tensor of high degree in some truncated or lossy compressed format. We look at
some common post-processing tasks which are not obvious in the compressed
format, as such huge data sets can not be stored in their entirety, and the
value of an element is not readily accessible through simple look-up. The tasks
we consider are finding the location of maximum or minimum, or minimum and
maximum of a function of the data, or finding the indices of all elements in
some interval --- i.e. level sets, the number of elements with a value in such
a level set, the probability of an element being in a particular level set, and
the mean and variance of the total collection.
  The algorithms to be described are fixed point iterations of particular
functions of the tensor, which will then exhibit the desired result. For this,
the data is considered as an element of a high degree tensor space, although in
an abstract sense, the algorithms are independent of the representation of the
data as a tensor. All that we require is that the data can be considered as an
element of an associative, commutative algebra with an inner product. Such an
algebra is isomorphic to a commutative sub-algebra of the usual matrix algebra,
allowing the use of matrix algorithms to accomplish the mentioned tasks. We
allow the actual computational representation to be a lossy compression, and we
allow the algebra operations to be performed in an approximate fashion, so as
to maintain a high compression level. One such example which we address
explicitly is the representation of data as a tensor with compression in the
form of a low-rank representation.

Numerical Analysis;Data Structures and Algorithms;Numerical Analysis;Computation