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and where n is the overall number of data points. For a least trimmed squares analysis, this objective function is replaced by one constructed in the following way. For a fixed value of β, let () denote the set of ordered absolute values of the residuals (in increasing order of absolute value). In this notation, the standard sum of squares ...
The running time is of order (), since there are subsets and, to check each subset, we need to sum at most n elements. The algorithm can be implemented by depth-first search of a binary tree: each level in the tree corresponds to an input number; the left branch corresponds to excluding the number from the set, and the right branch corresponds ...
The critical value corresponds to the cumulative distribution function of the F distribution with x equal to the desired confidence level, and degrees of freedom d 1 = (n − p) and d 2 = (N − n). The assumptions of normal distribution of errors and independence can be shown to entail that this lack-of-fit test is the likelihood-ratio test of ...
In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S). In multiway number partitioning , there is an integer parameter k , and the goal is to decide whether S can be partitioned into k subsets of equal sum ...
The algorithm performs summation with two accumulators: sum holds the sum, and c accumulates the parts not assimilated into sum, to nudge the low-order part of sum the next time around. Thus the summation proceeds with "guard digits" in c , which is better than not having any, but is not as good as performing the calculations with double the ...
In computational complexity theory, the 3SUM problem asks if a given set of real numbers contains three elements that sum to zero. A generalized version, k-SUM, asks the same question on k elements, rather than simply 3. 3SUM can be easily solved in () time, and matching (⌈ / ⌉) lower bounds are known in some specialized models of computation (Erickson 1999).
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.
Python's is operator may be used to compare object identities (comparison by reference), and comparisons may be chained—for example, a <= b <= c. Python uses and, or, and not as Boolean operators. Python has a type of expression named a list comprehension, and a more general expression named a generator expression. [78]