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which can be used to evaluatefzQ) :06287686, which represents relative error of a t :93Vo The complete cubicpolynomialis shownin Fig 156

Numbers tables are also handy if you need to split delimited strings. Take, for example, the following string: 'Z,X,A,B,D,F,Z,Z,Z,Z,A,V,S,Q,L,B,B,B,B,B'. You want to get all the characters in that string without duplicates. This is easily accomplished with a numbers table. First, create the stored procedure in listing 8.

15,24

CREATE PROCEDURE SplitString @StringToSplit varchar(1000), @Delimiter varchar(10) AS SELECT DISTINCT SUBSTRING(@Delimiter + @StringToSplit + @Delimiter, number + 1, CHARINDEX(@Delimiter, @Delimiter + @StringToSplit + @Delimiter, number + 1) - number -1) As StringItem FROM Numbers WHERE number <= LEN(@Delimiter + @StringToSplit + @Delimiter) - 1 AND SUBSTRING(@Delimiter + @StringToSplit + @Delimiter, number, 1) = @Delimiter ORDER BY StringItem GO

It is straightforward developan M-file to implementNewtoninterpolation in Fig157, to As the first step is to compute the finite divided differencesand storethem in an array difThe ferences then usedin conjunctionwith Eq (1518)to per-form interpolation are the An exampleof a session using the function would be to duplicatethe calculation we just performed Exarnple153: in

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ness The introduction of computers alone has created myriad changes For example, in engineering, innumerable mechanical engineers have had to be reoriented to electrical engineering Retraining that is less sophisticated but encompasses many more people has taken place with clerical and accounting employees In a brief period, the computer has transformed of ces, not only by replacing the typewriter but also by radically changing how data are aggregated, stored, duplicated, and presented The existence of private-sector careers in training and development is one of the best-kept secrets in American society That is dif cult to understand, given that thousands of people are teaching in the private sector and huge sums of money are being spent in the effort It is predicted that threefourths of all currently employed workers will need retraining throughout the twenty- rst century During this century, millions of manufacturing jobs will be restructured The American Society for Training and Development (ASTD) is one of the best sources of information on employer-provided workplace learning and the educators who train employees It annually surveys trends in workplace learning and performance The 2002 report State of the Industry says that private-sector employers spent $542 billion on formal training The highest expenditures were in nance, insurance, and real estate; transportation and public utilities; and technology On the basis of spending per eligible employee, nondurable manufacturing spent the most In 2000, in the 367 organizations (out of 1,000) that responded to ASTD s survey, about 87 percent of eligible employees in the civilian workforce received formal employer-provided training Among eligible employees the greatest needs for training were information technology skills, managerial/supervisory skills, technical processes and procedures, occupational safety, and product knowledge Training in business and industry is conducted almost entirely for the bene t of the organization that is, for what it will do to improve employee performance, productivity, service, and pro t Training runs the gamut from upgrading the skills and work style of technicians and blue-collar workers to training supervisors and executives in better, more ef cient, more effective methods of management Leaders in business and industry also recognize the need to restore pride in work and product That goal becomes even more important when team building that is, learning to work cooperatively with other people proves to be an important factor in the quality of production or service.

= Newtint(x,y,xx) function yint polynomial I'Jewton interpolal-ing % Newtint: = llewtrnt(x,y,xx): Uses an (n - 1)-order Newton yint ,x, yl polynrmial inr erpofdtrng "o bosed or n dala poinrs lyrnt) % to determine a vafue of the dependent variable at a given value of the independenc variable, xx % % input: :-lanor F va ' ' rh'c 1Fr x%

Here s how you d call that stored procedure with a string delimited with commas:

output yint %

EXEC SplitString 'Z,X,A,B,D,F,Z,Z,Z,Z,A,V,S,Q,L,B,B,B,B,B',','

!} omnrl e rlre finir-e % difference table n = length(x);

hri:

Here s an example with a pipe symbol as delimiter:

b = zeros (n,n) ; assign dependenL variables to the first column of b = y(:); b(:,1) % the (:) ensur:es that y is a column vector for j - 2,n for i = 1:n j+1- (b(i+1,j-1)-b(i,j-1))/(x(i+j-r)-x(i)) b(i,j) ; end end use Lhe finite

The same code from the stored procedure, but with comments explaining how it works, is shown in listing 10.

1ts , 1 -

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