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In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist John M. Pollard , in the same paper as his better-known Pollard's rho algorithm for ...
Alternately, a function may be considered as a lambda term defined purely in lambda calculus. These different approaches affect how a mathematician and a programmer may regard a fixed-point combinator. A mathematician may see the Y combinator applied to a function as being an expression satisfying the fixed-point equation, and therefore a solution.
The algorithm performs a binary search to find the minimal threshold for which a solution still exists: this gives the minimal solution to the SDP problem. The quantum algorithm provides a quadratic improvement over the best classical algorithm in the general case, and an exponential improvement when the input matrices are of low rank .
For example, in simply typed lambda calculus, it is a theorem that every evaluation strategy terminates for every simply typed lambda-term, whereas evaluation of untyped lambda-terms need not terminate (see below). One reason there are many different typed lambda calculi has been the desire to do more (of what the untyped calculus can do ...
Matrix pencils play an important role in numerical linear algebra.The problem of finding the eigenvalues of a pencil is called the generalized eigenvalue problem.The most popular algorithm for this task is the QZ algorithm, which is an implicit version of the QR algorithm to solve the eigenvalue problem = without inverting the matrix (which is impossible when is singular, or numerically ...
The key idea behind the algorithm is to find an expression of the loss function for the Wahba's problem as a quadratic form, using the Cayley–Hamilton theorem and the Newton–Raphson method to efficiently solve the eigenvalue problem and construct a numerically stable representation of the solution.
One of the key principles of dictionary learning is that the dictionary has to be inferred from the input data. The emergence of sparse dictionary learning methods was stimulated by the fact that in signal processing , one typically wants to represent the input data using a minimal amount of components.
In this example, the lambda expression (lambda (book) (>= (book-sales book) threshold)) appears within the function best-selling-books. When the lambda expression is evaluated, Scheme creates a closure consisting of the code for the lambda expression and a reference to the threshold variable, which is a free variable inside the lambda expression.