Grease and flour three 8x1-1/2-inch round baking pans; set aside. Combine flour, baking powder, and baking soda; set aside.
In a large mixing bowl beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add sugar; beat until fluffy. Add egg yolks and vanilla; beat on medium speed until combined. Add flour mixture and buttermilk alternately to egg yolk mixture, beating on low speed after each addition just until combined. Fold in coconut and chopped pecans.
Thoroughly wash the beaters. In a small mixing bowl beat egg whites until stiff peaks form (tips stand straight). Fold about one-third of the egg whites into cake batter to lighten. Fold in remaining whites. Spread batter evenly into prepared pans.
Bake in a 350 degree F oven for 25 to 30 minutes or until a wooden toothpick inserted near centers comes out clean. Cool in pans on wire racks 10 minutes; remove from pans. Cool thoroughly on racks.
When cool, spread the top of a cake layer with frosting. Top with another layer, frost, and top with a third layer. Frost top and sides of cake with remaining frosting. If desired, decorate cake with pecan halves. Chill cake until serving time. Store any leftover cake, covered, in the refrigerator up to 2 days. Makes 14 servings.
In a bowl beat cream cheese, softened; butter, softened; and vanilla until smooth. Gradually add sifted powdered sugar, beating until smooth. Stir in chopped pecans. Makes 4 cups.