It is known that the space of real valued, continuous functions C(B) over a multidimensional compact domain B ⊂ R , k ≥ 2 does not admit Haar spaces, which means that interpolation problems in finite… (More)

COMPUTING QUATERNIONIC ROOTS BY NEWTON’S METHOD DRAHOSLAVA JANOVSKÁ AND GERHARD OPFER Abstract. Newton’s method for finding zeros is formally adapted to finding roots of Hamilton’s quaternions. Since… (More)

see, e.g., [6, pp. 268-269], that the matrix Cn is non-singular. Example 1.1. Let a > 0 and b be real scalars such that b/a is not a negative integer smaller than −1. Define the nodes si = ia + b and… (More)

We study the quaternionic linear system which is composed out of terms of the form ln(x) := ∑n p=1 apxbp with quaternionic constants ap, bp and a variable number n of terms. In the first place we… (More)

In a previous paper we investigated Givens transformations applied to quaternion valued matrices. Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of… (More)

Let A∈Km×n be a given rectangular matrix generally with complex elements. The well-known Givens rotations and Householder re ections are frequently used to perform a reduction of the matrix A to… (More)

We study quaternionic linear equations of type λm(x) := m j=1 b j xc j = e with quaternionic constants b j , c j , e and arbitrary positive integer m. For m = 2 the resulting equation is called… (More)

Let (a n ) be a strictly monotone and convergent sequence of real numbers. Necessary and sufficient conditions are given that the sequence (b n ) defined by $$b_n = \frac{{a_{n + 1} - k_n a_n }}{{1 -… (More)