Vector orthogonal relations. Vector QD-algorithm

✍ Scribed by J. Van Iseghem

• Book ID: 104338297
• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 366 KB
• Volume: 19
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(87)80019-5

✦ Synopsis

Vector-Pad6 approximants to a function F = (fl,---, fd) from C to C d have been defined, uniquely, without any auxiliary choice than the degrees of the numerator and the denominator (the same for all the components fi), as in the scalar case [1,5]. The denominators are associated to polynomials Pf, which are given by vector orthogonal properties (R) and which satisfy for each s, recurrence relations of order d + 1 (i.e. with d + 2 terms), called relations (D).

We study here consequences of (R) and (D): first we prove an algorithm similar to the generalized MNA-algorithm; then we define a vector QD-algorithm which links two diagonals (PT)r and (P7+1)~.

Conversely if a family (Pr)~ > 0 verifying (D) is given, it is possible to build (P])r > 0,~ > 0, and d linear functional s C a, a =1 ..... d, such that pO = p~ and (P]) verify the orthogonal relations (R), with respect to the C ~.