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In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions , vectors , matrices , polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
An index that is summed over is a summation index, in this case "i ". It is also called a dummy index since any symbol can replace "i " without changing the meaning of the expression (provided that it does not collide with other index symbols in the same term). An index that is not summed over is a free index and should appear only once per ...
var c = 0.0 // The array input has elements indexed for i = 1 to input.length do // c is zero the first time around. var y = input[i] + c // sum + c is an approximation to the exact sum. (sum,c) = Fast2Sum(sum,y) // Next time around, the lost low part will be added to y in a fresh attempt. next i return sum
where i is the index of summation; a i is an indexed variable representing each term of the sum; m is the lower bound of summation, and n is the upper bound of summation. With {{ math }} [ edit ]
In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.
This is the modular sum of the values taken by the simple checksum as each block of the data word is added to it. The modulus used is the same. So, for each block of the data word, taken in sequence, the block's value is added to the first sum and the new value of the first sum is then added to the second sum.