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In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation.
Let = be the number of bits in the signals and , where = is a power of two. Divide the signals a {\displaystyle a} and b {\displaystyle b} into D {\displaystyle D} blocks of M {\displaystyle M} bits each, storing the resulting blocks as arrays A , B {\displaystyle A,B} (whose entries we shall consider for simplicity as arbitrary precision ...
jblas is a linear algebra library, created by Mikio Braun, for the Java programming language built upon BLAS and LAPACK. Unlike most other Java linear algebra libraries, jblas is designed to be used with native code through the Java Native Interface and comes with precompiled binaries. When used on one of the targeted architectures, it will ...
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication.
If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
Johnny Depp's attorneys are looking back at his tricky testimony during his trial with Amber Heard.. Two of the actor's lawyers, Benjamin Chew and Jessica Meyers, shed light on the 2022 Virginia ...
Computing the k th power of a matrix needs k – 1 times the time of a single matrix multiplication, if it is done with the trivial algorithm (repeated multiplication). As this may be very time consuming, one generally prefers using exponentiation by squaring , which requires less than 2 log 2 k matrix multiplications, and is therefore much ...