## About generation of number sequences in SQL Server page 2 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

## B. About Fibonacci sequenceThe Fibonacci sequence might be calculated by this iteration formula: A[i+2] = A[i] + A[i+1]; i = 1,…, n; A[1] = A[2] = 1. It`s simple to see the analogy with general case in previous point if we bring in function f(x,y)=x+y. The [iter] column is used for keeping iteration`s number, [a] column is used for keeping A[i], [b] and [c] for A[i+1] and A[i+2] correspondingly. The [d] column is not in use. The calculation of Fibonacci numbers may be put into code accordingly to general method like this:
Let`s give the result of query for calculation Fibonacci numbers are less than 1000 (2nd column).
## C. Equation`s root findingThe large section of mathematical and functional analysis is dedicated to finding equations` roots of one-variable and multivariable functions. The root of equation g(x) = 0 is a number r (or vector r) which complies with condition g(r) = 0. The general method of solving such equations is in reduction to the problem of fixed point: x=f(x). The sense of this reduction is in the finding of such function f which makes equations g(x) = 0 and x = f(x) equivalent. Besides, operator f must be contracting. That is if the value r1 takes place near solution r, than the value r2 = f(r1) must be even nearer to the solution: abs(r-r2) < A * abs(r-r1), where positive constant A is less then unity (A<1) and isn`t depends on select of r1 value. The contracting mappings are possible be many. The preference ones are that for which A constant takes less value. The less the constant the process of finding of equation`s g(x) root converges faster: r2 = f(r1), r3 = f(r2), r4 = f(r3) …Let`s note an illustrating example in SQL. |

aggregate functions
Airport
ALL
AND
AS keyword
ASCII
AVG
Battles
Bezhaev
Bismarck
C.J.Date
calculated columns
Cartesian product
CASE
cast
CHAR
CHARINDEX
Chebykin
check constraint
classes
COALESCE
common table expressions
comparison predicates
Computer firm
CONSTRAINT
CONVERT
correlated subqueries
COUNT
CROSS APPLY
CTE
data type conversion
data types
database schema
DATEADD
DATEDIFF
DATENAME
DATEPART
DATETIME
date_time functions
DDL
DEFAULT
DEFAULT VALUES
DELETE
DISTINCT
DML
duplicates
edge
equi-join
EXCEPT
exercise (-2)
More tags

exercise 19
exercise 23
exercise 32
exercise 37
exercise 39
exercise 46
exercise 54
exercise 55
exercise 56
exercise 57
exercise 7
exercise 70
exercise 8
exercises
EXISTS
FLOAT
FOREIGN KEY
FROM
FULL JOIN
GROUP BY
grouping
Guadalcanal
HAVING
head ships
IDENTITY
IN
income
INFORMATION_SCHEMA
inner join
INSERT
INTERSECT
IS NOT NULL
IS NULL
ISNULL
join operations
laptop
launched year
LEFT
LEFT OUTER JOIN
LEN
LIKE
LTRIM
MAX
MIN
mistakes
money
MySQL
NATURAL JOIN
node
NOT
NOT IN
NULL
NULLIF
number sequences
number-sequence generation
numbering
ON DELETE CASCADE
OR
Oracle
ORDER BY
outcome
Outcomes
outer joins
OVER
paging
Painting
PARTITION BY
Pass_in_trip
PATINDEX
PC
PIVOT
PostgreSQL
predicates
primary key
printer
Product
Ranking functions
recursive CTE
renaming columns
REPLACE
RIGHT
RIGHT JOIN
ROUND
rounding
ROW_NUMBER
ships
sorting
SQL Server
SQL Server 2012
SQL-92
sql-ex.ru
string functions
subquery
SUBSTRING
SUM
tables join
tips and solutions
Torus
Transact-SQL
Trip
TRUNCATE TABLE
type conversion
UNION
UNION ALL
UNKNOWN
UNPIVOT
UPDATE
varchar
WHERE
window functions
WITH
XML
XPath
XQuery

The book was updated

*several days ago*