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Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
The quantity is called the relative redundancy and gives the maximum possible data compression ratio, when expressed as the percentage by which a file size can be decreased. (When expressed as a ratio of original file size to compressed file size, the quantity R : r {\displaystyle R:r} gives the maximum compression ratio that can be achieved.)
A logical spreadsheet is a spreadsheet in which formulas take the form of logical constraints rather than function definitions.. In traditional spreadsheet systems, such as Excel, cells are partitioned into "directly specified" cells and "computed" cells and the formulas used to specify the values of computed cells are "functional", i.e. for every combination of values of the directly ...
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is + = (), =,,, … which gives rise to the sequence,,, … of iterated function applications , (), (()), … which is hoped to converge to a point .
In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...
Free and open-source software portal; Pyspread is a non-traditional spreadsheet.Cells in pyspread's grid accept expressions in the Python programming language. [2] A cell can return any Python object, which allows calculations with vectors, matrices, fractions, arbitrary precision numbers and symbols.
Theorem — If ⌈ ((+)) ⌉ then the following is true for every encoding and decoding function : {,} {,} and : {,} {,} respectively: [(() +)]. The intuition behind the proof is however showing the number of errors to grow rapidly as the rate grows beyond the channel capacity.
The theorem is named after Soviet Ukrainian mathematicians Volodymyr Marchenko and Leonid Pastur who proved this result in 1967. If X {\displaystyle X} denotes a m × n {\displaystyle m\times n} random matrix whose entries are independent identically distributed random variables with mean 0 and variance σ 2 < ∞ {\displaystyle \sigma ^{2 ...