Linear equations and interpolation in Boolean algebra

Differential Equations and Linear Algebra

where D = d/dt is the basic differentiation operator on functions. (The j-th derivative operator, for j ≥ 1, is Dj , and we consider the identity operator I as D0, since it is standard to regard the zero-th derivative of a function as the function itself: D0(y) = y for all functions y.) We call (1.2) an n-th order linear differential operator since the highest derivative appearing in it is the ...

Differential Equations and Linear Algebra Notes

Algorithms for Verifying Variants of Boolean Algebra Equations and Expressions

The word, Boolean, was derived from the name of a British mathematician, George Boole, as a result of his classical work on logic. Boolean algebra can be defined as a set, whose members have two possible values, with two binary operators and one unary operator, satisfying the properties of commutativity, associativity, distributivity, existence of identity and complement. Boolean algebra has im...

LINEAR ALGEBRA AND ZTSAPPLZCATZONS 10 , 111 - 128 ( 1975 ) Boolean

In this paper we consider a variety of questions in the context of Boolean designs. For example, ErdGs asked: How many subsets of an n-set can be found so that pairwise their intersections are all even (odd)? E. Berlekamp [2] and the author both answered this question; the answer is approximately 2[b”‘. Another question which can be formulated in terms of Boolean designs was asked by J. A. Bond...

Numerical linear algebra techniques for efficient RBFs interpolation and collocation

Scattered data interpolation using Radial Basis Functions (RBFs) involves solving ill-conditioned Symmetric Positive Definite (SPD) linear systems; refer e.g. to [6] for further details. We will discuss the properties (conditioning, density) of the interpolation matrices for both global and compactly supported kernels, depending on the value of the shape parameter for both classical global inte...