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The total complexity is thus , or if ; the Lanczos algorithm can be very fast for sparse matrices. Schemes for improving numerical stability are typically judged against this high performance. The vectors are called Lanczos vectors. The vector is not used after is computed, and the vector is not used after is computed.
The logical size and capacity of the final array are shown. In computer science, a dynamic array, growable array, resizable array, dynamic table, mutable array, or array list is a random access, variable-size list data structure that allows elements to be added or removed. It is supplied with standard libraries in many modern mainstream ...
Vector space. Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2w. In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and ...
A bit array (also known as bitmask, [ 1] bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to implement a simple set data structure. A bit array is effective at exploiting bit-level parallelism in hardware to perform operations quickly. A typical bit array stores kw bits, where w ...
Array (data type) In computer science, array is a data type that represents a collection of elements ( values or variables ), each selected by one or more indices (identifying keys) that can be computed at run time during program execution. Such a collection is usually called an array variable or array value. [ 1]
C++ Standard Library. The Standard Template Library ( STL) is a software library originally designed by Alexander Stepanov for the C++ programming language that influenced many parts of the C++ Standard Library. It provides four components called algorithms, containers, functions, and iterators. [ 1]
Vector space model. Vector space model or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the distance between vectors represents the relevance between the documents. It is used in information filtering, information retrieval, indexing and relevancy rankings.
Rodrigues' rotation formula. In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix in SO (3), the group ...